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class="col col--9 col--offset-1" itemscope="" itemtype="http://schema.org/Blog"><article class=""><header><nav class="theme-doc-breadcrumbs breadcrumbsContainer_RLvU" aria-label="Breadcrumbs"><ul class="breadcrumbs" itemscope="" itemtype="https://schema.org/BreadcrumbList"><a class="breadcrumbs__item" href="/blog"><span class="lsd-typography lsd-typography--body3">All posts</span></a><li itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item breadcrumbs__item--active"><span class="lsd-typography lsd-typography--body3 breadcrumbs__link" itemprop="name">GossipSub Improvements: Evolution of Overlay Design and Message Dissemination in Unstructured P2P Networks</span><meta itemprop="position" content="1"></li></ul></nav><h1 class="title_f1Hy">GossipSub Improvements: Evolution of Overlay Design and Message Dissemination in Unstructured P2P Networks</h1><div class="container_PkUo margin-vert--md"><time datetime="2023-11-06T12:00:00.000Z" itemprop="datePublished">November 6, 2023</time><div class="authors_dZ4g"><span class="lsd-typography lsd-typography--body2">by </span><div class="col col--6 authorCol_y4tx"><div class="avatar margin-bottom--sm"><div class="avatar__intro" itemprop="author" itemscope="" itemtype="https://schema.org/Person"><div class="avatar__name"><span class="lsd-typography lsd-typography--body2" itemprop="name">Umar Farooq</span></div></div></div></div></div><div>14 min read</div></div><hr class="blog-divider"></header><div id="__blog-post-container" class="markdown"><p>GossipSub Improvements: Evolution of Overlay Design and Message Dissemination in Unstructured P2P Networks</p>
<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="motivitation">Motivitation<a href="#motivitation" class="hash-link" aria-label="Direct link to Motivitation" title="Direct link to Motivitation">​</a></h2>
<p>We have been recently working on analyzing and improving the performance of the GossipSub protocol for large messages,
as in the case of Ethereum Improvement Proposal <a href="https://eips.ethereum.org/EIPS/eip-4844" target="_blank" rel="noopener noreferrer">EIP-4844</a>.
This work led to a comprehensive study of unstructured P2P networks.
The intention was to identify the best practices that can serve as guidelines for performance improvement and scalability of P2P networks.</p>
<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="introduction">Introduction<a href="#introduction" class="hash-link" aria-label="Direct link to Introduction" title="Direct link to Introduction">​</a></h2>
<p>Nodes in an unstructured p2p network form self-organizing overlay(s) on top of the IP infrastructure to facilitate different services like information dissemination,
query propagation, file sharing, etc. The overlay(s) can be as optimal as a tree-like structure or as enforcing as a fully connected mesh.</p>
<p>Due to peer autonomy and a trustless computing environment, some peers may deviate from the expected operation or even leave the network.
At the same time, the underlying IP layer is unreliable.</p>
<p>Therefore, tree-like overlays are not best suited for reliable information propagation.
Moreover, tree-based solutions usually result in significantly higher message dissemination latency due to suboptimal branches.</p>
<p>Flooding-based solutions, on the other hand, result in maximum resilience against adversaries and achieve minimal message dissemination latency because the message propagates through all (including the optimal) paths.
Redundant transmissions help maintain the integrity and security of the network in the presence of adversaries and high node failure but significantly increase network-wide bandwidth utilization, cramming the bottleneck links.</p>
<p>An efficient alternative is to lower the number of redundant transmissions by D-regular broadcasting, where a peer will likely receive (or relay) a message from up to <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi></mrow><annotation encoding="application/x-tex">D</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.02778em">D</span></span></span></span> random peers.
Publishing through a D-regular overlay triggers approximately <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>N</mi><mo>×</mo><mi>D</mi></mrow><annotation encoding="application/x-tex">N \times D</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7667em;vertical-align:-0.0833em"></span><span class="mord mathnormal" style="margin-right:0.10903em">N</span><span class="mspace" style="margin-right:0.2222em"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em"></span></span><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.02778em">D</span></span></span></span> transmissions.
Reducing <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi></mrow><annotation encoding="application/x-tex">D</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.02778em">D</span></span></span></span> reduces the redundant transmissions but compromises reachability and latency.
Sharing metadata through a K-regular overlay (where <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>K</mi><mo>&gt;</mo><mi>D</mi></mrow><annotation encoding="application/x-tex">K &gt; D</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7224em;vertical-align:-0.0391em"></span><span class="mord mathnormal" style="margin-right:0.07153em">K</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.02778em">D</span></span></span></span>) allows nodes to pull missing messages.</p>
<p>GossipSub [<a href="https://arxiv.org/pdf/2007.02754.pdf" target="_blank" rel="noopener noreferrer">1</a>] benefits from full-message (D-regular) and metadata-only (k-regular) overlays.
Alternatively, a metadata-only overlay can be used, requiring a pull-based operation that significantly minimizes bandwidth utilization at the cost of increased latency.</p>
<p>Striking the right balance between parameters like <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mo separator="true">,</mo><mi>K</mi></mrow><annotation encoding="application/x-tex">D, K</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8778em;vertical-align:-0.1944em"></span><span class="mord mathnormal" style="margin-right:0.02778em">D</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord mathnormal" style="margin-right:0.07153em">K</span></span></span></span>, pull-based operation, etc., can yield application-specific performance tuning, but scalability remains a problem.</p>
<p>At the same time, many other aspects can significantly contribute to the network&#x27;s performance and scalability.
One option is to realize peers&#x27; suitability and continuously changing capabilities while forming overlays.</p>
<p>For instance, a low-bandwidth link near a publisher can significantly demean the entire network&#x27;s performance.
Reshuffling of peering links according to the changing network conditions can lead to superior performance.</p>
<p>Laying off additional responsibilities to more capable nodes (super nodes) can alleviate peer cramming, but it makes the network susceptible to adversaries/peer churn.
Grouping multiple super nodes to form virtual node(s) can solve this problem.</p>
<p>Similarly, flat (single-tier) overlays cannot address the routing needs in large (geographically dispersed) networks.</p>
<p>Hierarchical (Multi-tier) overlays with different intra/inter-overlay routing solutions can better address these needs.
Moreover, using message aggregation schemes for grouping multiple messages can save bandwidth and provide better resilience against adversaries/peer churn.</p>
<p>This article&#x27;s primary objective is to investigate the possible choices that can empower an unstructured P2P network to achieve superior performance for the broadest set of applications.
We look into different constraints imposed by application-specific needs (performance goals) and investigate various choices that can augment the network&#x27;s performance.
We explore overlay designs/freshness, peer selection approaches, message-relaying mechanisms, and resilience against adversaries/peer churn.
We consider GossipSub a baseline protocol to explore various possibilities and decisively commit to the ones demonstrating superior performance.
We also discuss the current state and, where applicable, propose a strategic plan for embedding new features to the GossipSub protocol.</p>
<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="goal1-low-latency-operation">GOAL1: Low Latency Operation<a href="#goal1-low-latency-operation" class="hash-link" aria-label="Direct link to GOAL1: Low Latency Operation" title="Direct link to GOAL1: Low Latency Operation">​</a></h2>
<p>Different applications, like blockchain, streaming, etc., impose strict time bounds on network-wide message dissemination latency.
A message delivered after the imposed time bounds is considered as dropped.
An early message delivery in applications like live streaming can further enhance the viewing quality.</p>
<p>The properties and nature of the overlay network topology significantly impact the performance of services and applications executed on top of them.
Studying and devising mechanisms for better overlay design and message dissemination is paramount to achieving superior performance.</p>
<p>Interestingly, shortest-path message delivery trees have many limitations:</p>
<ol>
<li>Changing network dynamics requires a quicker and continuous readjustment of the multicast tree.</li>
<li>The presence of resource-constrained (bandwidth/compute, etc.) nodes in the overlay can result in congestion.</li>
<li>Node failure can result in partitions, making many segments unreachable.</li>
<li>Assuring a shortest-path tree-like structure requires a detailed view of the underlying (and continuously changing) network topology.</li>
</ol>
<p>Solutions involve creating multiple random trees to add redundancy [<a href="https://ieeexplore.ieee.org/abstract/document/6267905" target="_blank" rel="noopener noreferrer">2</a>].
Alternatives involve building an overlay mesh and forwarding messages through the multicast delivery tree (eager push).</p>
<p>Metadata is shared through the overlay links so that the nodes can ask for missing messages (lazy push or pull-based operation) through the overlay links.
New nodes are added from the overlay on node failure, but it requires non-faulty node selection.</p>
<p>GossipSub uses eager push (through overlay mesh) and lazy push (through IWANT messages).</p>
<p>The mesh degree <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>D</mi><mrow><mi>L</mi><mi>o</mi><mi>w</mi></mrow></msub><mo>≤</mo><mi>D</mi><mo>≤</mo><msub><mi>D</mi><mrow><mi>H</mi><mi>i</mi><mi>g</mi><mi>h</mi></mrow></msub></mrow><annotation encoding="application/x-tex">D_{Low} \leq D \leq D_{High}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">L</span><span class="mord mathnormal mtight">o</span><span class="mord mathnormal mtight" style="margin-right:0.02691em">w</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.8193em;vertical-align:-0.136em"></span><span class="mord mathnormal" style="margin-right:0.02778em">D</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.9694em;vertical-align:-0.2861em"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.08125em">H</span><span class="mord mathnormal mtight">i</span><span class="mord mathnormal mtight" style="margin-right:0.03588em">g</span><span class="mord mathnormal mtight">h</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em"><span></span></span></span></span></span></span></span></span></span> is crucial in deciding message dissemination latency.
A smaller value for <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi></mrow><annotation encoding="application/x-tex">D</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.02778em">D</span></span></span></span> results in higher latency due to increased rounds, whereas a higher <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi></mrow><annotation encoding="application/x-tex">D</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.02778em">D</span></span></span></span> reduces latency on the cost of increased bandwidth.
At the same time, keeping <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi></mrow><annotation encoding="application/x-tex">D</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.02778em">D</span></span></span></span> independent of the growing network size (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>N</mi></mrow><annotation encoding="application/x-tex">N</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.10903em">N</span></span></span></span>) may increase network-wide message dissemination latency.
Adjusting <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi></mrow><annotation encoding="application/x-tex">D</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.02778em">D</span></span></span></span> with <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>N</mi></mrow><annotation encoding="application/x-tex">N</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.10903em">N</span></span></span></span> maintains similar latency on the cost of increased workload for peers.
Authors in [<a href="https://infoscience.epfl.ch/record/83478/files/EugGueKerMas04IEEEComp.pdf" target="_blank" rel="noopener noreferrer">3</a>] suggest only a logarithmic increase in <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi></mrow><annotation encoding="application/x-tex">D</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.02778em">D</span></span></span></span> to maintain a manageable workload for peers.
In [<a href="https://inria.hal.science/tel-02375909/document" target="_blank" rel="noopener noreferrer">4</a>], it is reported that the average mesh degree should not exceed <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>D</mi><mrow><mi>a</mi><mi>v</mi><mi>g</mi></mrow></msub><mo>=</mo><mi>ln</mi><mo>⁡</mo><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo><mo>+</mo><mi>C</mi></mrow><annotation encoding="application/x-tex">D_{avg} = \ln(N) + C</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9694em;vertical-align:-0.2861em"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight" style="margin-right:0.03588em">vg</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mop">ln</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.10903em">N</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em"></span></span><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.07153em">C</span></span></span></span> for an optimal operation,
where <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi></mrow><annotation encoding="application/x-tex">C</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.07153em">C</span></span></span></span> is a small constant.</p>
<p>Moreover, quicker shuffling of peers results in better performance in the presence of resource-constrained nodes or node failure [<a href="https://inria.hal.science/tel-02375909/document" target="_blank" rel="noopener noreferrer">4</a>].</p>
<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="goal2-considering-heterogeneity-in-overlay-design">GOAL2: Considering Heterogeneity In Overlay Design<a href="#goal2-considering-heterogeneity-in-overlay-design" class="hash-link" aria-label="Direct link to GOAL2: Considering Heterogeneity In Overlay Design" title="Direct link to GOAL2: Considering Heterogeneity In Overlay Design">​</a></h2>
<p>Random peering connections in P2P overlays represent a stochastic process. It is inherently difficult to precisely model the performance of such systems.
Most of the research on P2P networks provides simulation results assuming nodes with similar capabilities.
The aspect of dissimilar capabilities and resource-constrained nodes is less explored.</p>
<p>It is discussed in GOAL1 that overlay mesh results in better performance if <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>D</mi><mrow><mi>a</mi><mi>v</mi><mi>g</mi></mrow></msub></mrow><annotation encoding="application/x-tex">D_{avg}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9694em;vertical-align:-0.2861em"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight" style="margin-right:0.03588em">vg</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em"><span></span></span></span></span></span></span></span></span></span> does not exceed <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ln</mi><mo>⁡</mo><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo><mo>+</mo><mi>C</mi></mrow><annotation encoding="application/x-tex">\ln(N) + C</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mop">ln</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.10903em">N</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em"></span></span><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.07153em">C</span></span></span></span>.
Enforcing all the nodes to have approximately <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ln</mi><mo>⁡</mo><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo><mo>+</mo><mi>C</mi></mrow><annotation encoding="application/x-tex">\ln(N) + C</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mop">ln</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.10903em">N</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em"></span></span><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.07153em">C</span></span></span></span> peers makes resource-rich nodes under-utilized, while resource-constrained nodes are overloaded.
At the same time, connecting high-bandwidth nodes through a low-bandwidth node undermines the network&#x27;s performance.
Ideally, the workload on any node should not exceed its available resources.
A better solution involves a two-phased operation:</p>
<ol>
<li>
<p>Every node computes its available bandwidth and selects a node degree <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi></mrow><annotation encoding="application/x-tex">D</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.02778em">D</span></span></span></span> proportional to its available bandwidth [<a href="https://inria.hal.science/tel-02375909/document" target="_blank" rel="noopener noreferrer">4</a>].
Different bandwidth estimation approaches are suggested in literature [<a href="https://ieeexplore.ieee.org/abstract/document/1224454" target="_blank" rel="noopener noreferrer">5</a>,<a href="https://ieeexplore.ieee.org/abstract/document/1248658" target="_blank" rel="noopener noreferrer">6</a>].
Simple bandwidth estimation approaches like variable packet size probing [<a href="https://ieeexplore.ieee.org/abstract/document/1248658" target="_blank" rel="noopener noreferrer">6</a>] yield similar results with less complexity.
It is also worth mentioning that many nodes may want to allocate only a capped share of their bandwidth to the network.
Lowering <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi></mrow><annotation encoding="application/x-tex">D</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.02778em">D</span></span></span></span> according to the available bandwidth can still prove helpful.
Additionally, bandwidth preservation at the transport layer through approaches like µTP can be useful.
To further conform to the suggested mesh-degree average <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>D</mi><mrow><mi>a</mi><mi>v</mi><mi>g</mi></mrow></msub></mrow><annotation encoding="application/x-tex">D_{avg}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9694em;vertical-align:-0.2861em"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight" style="margin-right:0.03588em">vg</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em"><span></span></span></span></span></span></span></span></span></span>, every node tries achieving this average within its neighborhood, resulting in an overall similar <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>D</mi><mrow><mi>a</mi><mi>v</mi><mi>g</mi></mrow></msub></mrow><annotation encoding="application/x-tex">D_{avg}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9694em;vertical-align:-0.2861em"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight" style="margin-right:0.03588em">vg</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em"><span></span></span></span></span></span></span></span></span></span>.</p>
</li>
<li>
<p>From the available local view, every node tries connecting peers with the lowest latency until <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi></mrow><annotation encoding="application/x-tex">D</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.02778em">D</span></span></span></span> connections are made.
We suggest referring to the peering solution discussed in GOAL5 to avoid network partitioning.</p>
</li>
</ol>
<p>The current GossipSub design considers homogeneous peers, and every node tries maintaining <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>D</mi><mrow><mi>L</mi><mi>o</mi><mi>w</mi></mrow></msub><mo>≤</mo><mi>D</mi><mo>≤</mo><msub><mi>D</mi><mrow><mi>H</mi><mi>i</mi><mi>g</mi><mi>h</mi></mrow></msub></mrow><annotation encoding="application/x-tex">D_{Low} \leq D \leq D_{High}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">L</span><span class="mord mathnormal mtight">o</span><span class="mord mathnormal mtight" style="margin-right:0.02691em">w</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.8193em;vertical-align:-0.136em"></span><span class="mord mathnormal" style="margin-right:0.02778em">D</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.9694em;vertical-align:-0.2861em"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.08125em">H</span><span class="mord mathnormal mtight">i</span><span class="mord mathnormal mtight" style="margin-right:0.03588em">g</span><span class="mord mathnormal mtight">h</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em"><span></span></span></span></span></span></span></span></span></span> connections.</p>
<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="goal3-bandwidth-optimization">GOAL3: Bandwidth Optimization<a href="#goal3-bandwidth-optimization" class="hash-link" aria-label="Direct link to GOAL3: Bandwidth Optimization" title="Direct link to GOAL3: Bandwidth Optimization">​</a></h2>
<p>Redundant message transmissions are essential for handling adversaries/node failure. However, these transmissions result in traffic bursts, cramming many overlay links.
This not only adds to the network-wide message dissemination latency but a significant share of the network&#x27;s bandwidth is wasted on (usually) unnecessary transmissions.
It is essential to explore solutions that can minimize the number of redundant transmissions while assuring resilience against node failures.</p>
<p>Many efforts have been made to minimize the impact of redundant transmissions.
These solutions include multicast delivery trees, metadata sharing to enable pull-based operation, in-network information caching, etc. [<a href="https://dl.acm.org/doi/abs/10.1145/945445.945473" target="_blank" rel="noopener noreferrer">7</a>,<a href="https://link.springer.com/chapter/10.1007/11558989_12" target="_blank" rel="noopener noreferrer">8</a>].
GossipSub employs a hybrid of eager push (message dissemination through the overlay) and lazy push (a pull-based operation by the nodes requiring information through IWANT messages).</p>
<p>A better alternative to simple redundant transmission is to use message aggregation [<a href="https://ieeexplore.ieee.org/abstract/document/8737576" target="_blank" rel="noopener noreferrer">9</a>,<a href="https://dl.acm.org/doi/abs/10.1145/1993636.1993676" target="_blank" rel="noopener noreferrer">10</a>,<a href="https://ieeexplore.ieee.org/abstract/document/4276446" target="_blank" rel="noopener noreferrer">11</a>] for the GossipSub protocol.
As a result, redundant message transmissions can serve as a critical advantage of the GossipSub protocol.
Suppose that we have three equal-length messages <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi><mn>1</mn><mo separator="true">,</mo><mi>x</mi><mn>2</mn><mo separator="true">,</mo><mi>x</mi><mn>3</mn></mrow><annotation encoding="application/x-tex">x1, x2, x3</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8389em;vertical-align:-0.1944em"></span><span class="mord mathnormal">x</span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord mathnormal">x</span><span class="mord">2</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord mathnormal">x</span><span class="mord">3</span></span></span></span>. Assuming an XOR coding function,
we know two trivial properties: <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi><mn>1</mn><mo>⊕</mo><mi>x</mi><mn>2</mn><mo>⊕</mo><mi>x</mi><mn>2</mn><mo>=</mo><mi>x</mi><mn>1</mn></mrow><annotation encoding="application/x-tex">x1 \oplus x2 \oplus x2 = x1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em"></span><span class="mord mathnormal">x</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em"></span><span class="mbin">⊕</span><span class="mspace" style="margin-right:0.2222em"></span></span><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em"></span><span class="mord mathnormal">x</span><span class="mord">2</span><span class="mspace" style="margin-right:0.2222em"></span><span class="mbin">⊕</span><span class="mspace" style="margin-right:0.2222em"></span></span><span class="base"><span class="strut" style="height:0.6444em"></span><span class="mord mathnormal">x</span><span class="mord">2</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.6444em"></span><span class="mord mathnormal">x</span><span class="mord">1</span></span></span></span> and <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">∣</mi><mi>x</mi><mn>1</mn><mi mathvariant="normal">∣</mi><mo>=</mo><mi mathvariant="normal">∣</mi><mi>x</mi><mn>1</mn><mo>⊕</mo><mi>x</mi><mn>2</mn><mo>⊕</mo><mi>x</mi><mn>2</mn><mi mathvariant="normal">∣</mi></mrow><annotation encoding="application/x-tex">\vert x1 \vert = \vert x1 \oplus x2 \oplus x2 \vert</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord">∣</span><span class="mord mathnormal">x</span><span class="mord">1∣</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord">∣</span><span class="mord mathnormal">x</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em"></span><span class="mbin">⊕</span><span class="mspace" style="margin-right:0.2222em"></span></span><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em"></span><span class="mord mathnormal">x</span><span class="mord">2</span><span class="mspace" style="margin-right:0.2222em"></span><span class="mbin">⊕</span><span class="mspace" style="margin-right:0.2222em"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord mathnormal">x</span><span class="mord">2∣</span></span></span></span>.</p>
<p>This implies that instead of sending messages individually, we can encode and transmit composite message(s) to the network.
The receiver can reconstruct the original message from encoded segments.
As a result, fewer transmissions are sufficient for sending more messages to the network.</p>
<p>However, sharing linear combinations of messages requires organizing messages in intervals,
and devising techniques to identify all messages belonging to each interval.
In addition, combining messages from different publishers requires more complex arrangements,
involving embedding publisher/message IDs, delayed forwarding (to accommodate more messages), and mechanisms to ensure the decoding of messages at all peers.
Careful application-specific need analysis can help decide the benefits against the added complexity.</p>
<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="goal4-handling-large-messages">GOAL4: Handling Large Messages<a href="#goal4-handling-large-messages" class="hash-link" aria-label="Direct link to GOAL4: Handling Large Messages" title="Direct link to GOAL4: Handling Large Messages">​</a></h2>
<p>Many applications require transferring large messages for their successful operation. For instance, database/blockchain transactions [<a href="https://eips.ethereum.org/EIPS/eip-4844" target="_blank" rel="noopener noreferrer">12</a>].
This introduces two challenges:</p>
<ol>
<li>Redundant large message transmissions result in severe network congestion.</li>
<li>Message transmissions follow a store/forward process at all peers, which is inefficient in the case of large messages.</li>
</ol>
<p>The above-mentioned challenges result in a noticeable increase in message dissemination latency and bandwidth wastage.
Most of the work done for handling large messages involves curtailing redundant transmissions using multicast delivery trees,
reducing the number of fanout nodes, employing in-network message caching, pull-based operation, etc.</p>
<p>Approaches like message aggregation also prove helpful in minimizing bandwidth wastage.</p>
<p>Our recent work on GossipSub improvements (still a work in progress) suggests the following solutions to deal with large message transmissions:</p>
<ol>
<li>
<p>Using IDontWant message proposal [<a href="https://github.com/libp2p/specs/pull/413" target="_blank" rel="noopener noreferrer">13</a>] and staggered sending.</p>
<p>IDontWant message helps curtail redundant transmissions by letting other peers know we have already received the message.
Staggered sending enables relaying the message to a short subset of peers in each round.
We argue that simultaneously relaying a message to all peers hampers the effectiveness of the IDontWant message.
Therefore, using the IDontWant message with staggered sending can yield better results by allowing timely reception and processing of IDontWant messages.</p>
</li>
<li>
<p>Message transmissions follow a store/forward process at all peers that is inefficient in the case of large messages.
We can parallelize message transmission by partitioning large messages into smaller fragments, letting intermediate peers relay these fragments as soon as they receive them.</p>
</li>
</ol>
<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="goal5-scalability">GOAL5: Scalability<a href="#goal5-scalability" class="hash-link" aria-label="Direct link to GOAL5: Scalability" title="Direct link to GOAL5: Scalability">​</a></h2>
<p>P2P networks are inherently scalable because every incoming node brings in bandwidth and compute resources.
In other words, we can keep adding nodes to the network as long as every incoming node brings at-least <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>R</mi><mo>×</mo><mi>D</mi></mrow><annotation encoding="application/x-tex">R \times D</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7667em;vertical-align:-0.0833em"></span><span class="mord mathnormal" style="margin-right:0.00773em">R</span><span class="mspace" style="margin-right:0.2222em"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em"></span></span><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.02778em">D</span></span></span></span> bandwidth,
where <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>R</mi></mrow><annotation encoding="application/x-tex">R</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.00773em">R</span></span></span></span> is average data arrival rate.
It is worth mentioning that network-wide message dissemination requires at-least <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">⌈</mo><msub><mrow><mi>log</mi><mo>⁡</mo></mrow><mi>D</mi></msub><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo><mo stretchy="false">⌉</mo></mrow><annotation encoding="application/x-tex">\lceil \log_D (N) \rceil</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mopen">⌈</span><span class="mop"><span class="mop">lo<span style="margin-right:0.01389em">g</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2342em"><span style="top:-2.4559em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em">D</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2441em"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.10903em">N</span><span class="mclose">)⌉</span></span></span></span> hops.
Therefore, increasing network size increases message dissemination latency, assuming D is independent of the network size.</p>
<p>Additionally, problems like peer churn, adversaries, heterogeneity, distributed operation, etc., significantly hamper the network&#x27;s performance.
Most efforts for bringing scalability to the P2P systems have focused on curtailing redundant transmissions and flat overlay adjustments.
Hierarchical overlay designs, on the other hand, are less explored.</p>
<p>Placing a logical structure in unstructured P2P systems can help scale P2P networks.</p>
<p>One possible solution is to use a hierarchical overlay inspired by the approaches [<a href="https://link.springer.com/article/10.1007/s12083-016-0460-5" target="_blank" rel="noopener noreferrer">14</a>,<a href="https://link.springer.com/chapter/10.1007/978-3-030-19223-5_16" target="_blank" rel="noopener noreferrer">15</a>,<a href="https://ieeexplore.ieee.org/abstract/document/9826458" target="_blank" rel="noopener noreferrer">16</a>].
An abstract operation of such overlay design is provided below:</p>
<ol>
<li>
<p>Clustering nodes based on locality, assuming that such peers will have relatively lower intra-cluster latency and higher bandwidth.
For this purpose, every node tries connecting peers with the lowest latency until <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi></mrow><annotation encoding="application/x-tex">D</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.02778em">D</span></span></span></span> connections are made or the cluster limit is reached.</p>
</li>
<li>
<p>A small subset of nodes having the highest bandwidth and compute resources is selected from each cluster.
These super nodes form a fully connected mesh and jointly act as a virtual node,
mitigating the problem of peer churn among super nodes.</p>
</li>
<li>
<p>Virtual nodes form a fully connected mesh to construct a hierarchical overlay.
Each virtual node is essentially a collection of super nodes;
a link to any of the constituent super nodes represents a link to the virtual node.</p>
</li>
<li>
<p>One possible idea is to use GossipSub for intra-cluster message dissemination and FloodSub for inter-cluster message dissemination.</p>
</li>
</ol>
<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="summary">Summary<a href="#summary" class="hash-link" aria-label="Direct link to Summary" title="Direct link to Summary">​</a></h2>
<p>Overlay acts as a virtual backbone for a P2P network. A flat overlay is more straightforward and allows effortless readjustment to application needs.
On the other hand, a hierarchical overlay can bring scalability at the cost of increased complexity.
Regardless of the overlay design, a continuous readjustment to appropriate peering links is essential for superior performance.
At the same time, bandwidth preservation (through message aggregation, caching at strategic locations, metadata sharing, pull-based operation, etc.) can help minimize latency.
However, problems like peer churn and in-network adversaries can be best alleviated through balanced redundant coverage, and frequent reshuffling of the peering links.</p>
<h1>References</h1>
<ul>
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<li>[8] V. Pai, K. Kumar, K. Tamilmani, V. Sambamurthy, and A. E. Mohr, “Chainsaw: Eliminating trees from overlay multicast,” in Peer-to-Peer Systems IV: 4th International Workshop, IPTPS 2005, Ithaca, NY, USA, February 24-25, 2005. Revised Selected Papers 4. Springer, 2005, pp. 127–140. Retrieved from <a href="https://link.springer.com/chapter/10.1007/11558989_12" target="_blank" rel="noopener noreferrer">https://link.springer.com/chapter/10.1007/11558989_12</a></li>
<li>[9] Y.-D. Bromberg, Q. Dufour, and D. Frey, “Multisource rumor spreading with network coding,” in IEEE INFOCOM 2019-IEEE Conference on Computer Communications. IEEE, 2019, pp. 2359–2367. Retrieved from <a href="https://ieeexplore.ieee.org/abstract/document/8737576" target="_blank" rel="noopener noreferrer">https://ieeexplore.ieee.org/abstract/document/8737576</a></li>
<li>[10] B. Haeupler, “Analyzing network coding gossip made easy,” in Proceedings of the forty-third annual ACM symposium on Theory of computing, 2011, pp. 293–302. Retrieved from <a href="https://dl.acm.org/doi/abs/10.1145/1993636.1993676" target="_blank" rel="noopener noreferrer">https://dl.acm.org/doi/abs/10.1145/1993636.1993676</a></li>
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<li>[13] A. Manning, “Gossipsub extension for epidemic meshes (v1.2.0),” 2022. Retrieved from <a href="https://github.com/libp2p/specs/pull/413" target="_blank" rel="noopener noreferrer">https://github.com/libp2p/specs/pull/413</a></li>
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