9 Search Results for "Cohen, Itay"

Document
DOI: 10.4230/LIPIcs.ITCS.2026.93
Analyzing the Economic Impact of Decentralization on Users

Authors: Amit Levy, S. Matthew Weinberg, and Chenghan Zhou

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
We model the ultimate price paid by users of a decentralized ledger as resulting from a two-stage game where Miners (/Proposers/etc.) first purchase blockspace via a Tullock contest, and then price that space to users. When analyzing our distributed ledger model, we find: - A characterization of all possible pure equilibria (although pure equilibria are not guaranteed to exist). - A natural sufficient condition, implied by Regularity (à la [Myerson, 1981]), for existence of a "market-clearing" pure equilibrium where Miners choose to sell all space allocated by the Distributed Ledger Protocol, and that this equilibrium is unique. - The market share of the largest miner is the relevant "measure of decentralization" to determine whether a market-clearing pure equilibrium exists. - Block rewards do not impact users' prices at equilibrium, when pure equilibria exist. But, higher block rewards can cause pure equilibria to exist. We also discuss aspects of our model and how they relate to blockchains deployed in practice. For example, only "patient" users (who are happy for their transactions to enter the blockchain under any miner) would enjoy the conclusions highlighted by our model, whereas "impatient" users (who are interested only for their transaction to be included in the very next block) still face monopoly pricing.
Cite as

Amit Levy, S. Matthew Weinberg, and Chenghan Zhou. Analyzing the Economic Impact of Decentralization on Users. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 93:1-93:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{levy_et_al:LIPIcs.ITCS.2026.93,
  author =	{Levy, Amit and Weinberg, S. Matthew and Zhou, Chenghan},
  title =	{{Analyzing the Economic Impact of Decentralization on Users}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{93:1--93:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.93},
  URN =		{urn:nbn:de:0030-drops-253805},
  doi =		{10.4230/LIPIcs.ITCS.2026.93},
  annote =	{Keywords: Blockchain, Cryptocurrency, Blockspace Markets, Decentralization, Distributed Ledgers, Equilibrium Analysis, Tullock Contests}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2025.24
On Time-Optimal, Fault-Tolerant Algorithms for Connected Consensus Beyond Grade Two

Authors: Alan Ernesto Arteaga Vázquez

Published in: LIPIcs, Volume 361, 29th International Conference on Principles of Distributed Systems (OPODIS 2025)

Abstract
A common question in the asynchronous model is whether some given notion of agreement between processes is achievable. Usually, we formalise such agreement notions in the form of agreement problems. Some of these problems also receive the name of coordination primitives. Several fault-tolerant algorithms in asynchronous systems rely upon the use of different primitives as building blocks, such as adopt-commit, crusader agreement, or graded broadcast. Recently, the connected consensus problem - a form of agreement over a specific family of graphs parametrised by a positive integer R- was introduced. This problem unifies the three mentioned primitives while extending them for multi-valued inputs. Moreover, the problem is equipped with a security condition called binding, which limits the effect of malicious processes over the decision of correct parties. While fault-tolerant connected consensus algorithms for R = 1 and R = 2 are known, the existence of algorithmic solutions for any positive integer parameter remained an open question. In this work, we introduce a pair of fault-tolerant algorithms for connected consensus when the R parameter is any positive integer. We introduce a crash-resilient algorithm, which is optimal with respect to the maximum number of possible faulty processes. Our second algorithm is resilient to Byzantine failures; whose failure-resilience is optimal for a specific class of algorithms. Both algorithms satisfy the binding property and match the best known time complexities achieved for the R = 1 and R = 2 cases, further achieving time optimality for the general case in the crash-failure setting, and asymptotic time optimality in the Byzantine scenario.
Cite as

Alan Ernesto Arteaga Vázquez. On Time-Optimal, Fault-Tolerant Algorithms for Connected Consensus Beyond Grade Two. In 29th International Conference on Principles of Distributed Systems (OPODIS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 361, pp. 24:1-24:28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{arteagavazquez:LIPIcs.OPODIS.2025.24,
  author =	{Arteaga V\'{a}zquez, Alan Ernesto},
  title =	{{On Time-Optimal, Fault-Tolerant Algorithms for Connected Consensus Beyond Grade Two}},
  booktitle =	{29th International Conference on Principles of Distributed Systems (OPODIS 2025)},
  pages =	{24:1--24:28},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-409-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{361},
  editor =	{Arusoaie, Andrei and Onica, Emanuel and Spear, Michael and Tucci-Piergiovanni, Sara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2025.24},
  URN =		{urn:nbn:de:0030-drops-251973},
  doi =		{10.4230/LIPIcs.OPODIS.2025.24},
  annote =	{Keywords: Approximate Agreement, Binding, Connected Consensus}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.43
New Approximate Distance Oracles and Their Applications

Authors: Avi Kadria and Liam Roditty

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
Let G = (V, E) be an undirected graph with n vertices and m edges, and let μ = m/n. A distance oracle is a data structure designed to answer approximate distance queries, with the goal of achieving low stretch, efficient space usage, and fast query time. While much of the prior work focused on distance oracles with constant query time, this paper presents a comprehensive study of distance oracles with non-constant query time. We explore the tradeoffs between space, stretch, and query time of distance oracles in various regimes. Specifically, we consider both weighted and unweighted graphs in the regimes of stretch < 2 and stretch ≥ 2. In addition, we demonstrate several applications of our new distance oracles to the n-Pairs Shortest Paths (n-PSP) problem and the All Nodes Shortest Cycles (ANSC) problem. Our main contributions are: - Weighted graphs: We present a new three-way trade-off between stretch, space, and query time, offering a natural extension of the classical Thorup–Zwick distance oracle [STOC’01 and JACM’05] to regimes with larger query time. Specifically, for any 0 < r < 1/2 and integer k ≥ 1, we construct a (2k(1 - 2r) - 1)-stretch distance oracle with Õ(m + n^{1 + 1/k}) space and Õ(μ n^r) query time. This construction provides an asymptotic improvement over the classical (2k - 1)-stretch and O(n^{1 + 1/k})-space tradeoff of Thorup and Zwick in sparse graphs, at the cost of increased query time. We also improve upon a result of Dalirrooyfard et al. [FOCS’22], who presented a (2k - 2)-stretch distance oracle with O(m + n^{1 + 1/k}) space and O(μ n^{1/k}) query time. In our oracle we reduce the stretch from (2k - 2) to (2k - 5) while preserving the same space and query time. - Unweighted graphs: We present a (2k - 5, 4 + 2_{odd})-approximation distance oracle with O(n^{1 + 1/k}) space and O(n^{1/k}) query time. This improves upon a (2k - 2, 2_{odd})-approximation distance oracle of Dalirrooyfard et al. [FOCS’22] while maintaining the same space and query time. We also present a distance oracle that given u,v ∈ V returns an estimate d̂(u,v) ≤ d(u,v) + 2⌈ d(u,v) / 3 ⌉ + 2, using O(n^{4/3 + 2ε}) space and O(n^{1 - 3ε}) query time. To the best of our knowledge, this is the first distance oracle that simultaneously achieves a multiplicative stretch < 2, and a space complexity O(n^{1.5 - α}), for some α > 0. - Applications for n-PSP and ANSC: We present an Õ(m^{1 - 1/(k+1)} n)-time algorithm for the n-PSP problem, that for every input pair ⟨s_i,t_i⟩, where i ∈ [n], returns an estimate d̂(s_i, t_i) such that d̂(s_i,t_i) ≤ d(s_i,t_i) + 2⌈d(s_i,t_i)/2k⌉. By allowing a small additive error, this result circumvents the conditional running time lower bound of Ω(m^{2 - 2/(k+1)} ⋅ n^{1/(k+1) - o(1)}), established by Dalirrooyfard et al. [FOCS’22] for achieving (1 + 1/k)-stretch. Additionally, we present an Õ(mn^{1 - 1/k})-time algorithm for the ANSC problem that computes, for every u ∈ V, an estimate ĉ_u such that ĉ_u ≤ SC(u) + 2⌈SC(u)/2(k - 1)⌉, where SC(u) denotes the length of the shortest cycle containing u. This improves upon the Õ(m^{2 - 2/k}n^{1/k})-time algorithm of Dalirrooyfard et al. [FOCS'22], while achieving the same approximation guarantee. We obtain our results by developing several new techniques, among them are the borderline vertices technique and the middle vertex technique, which may be of independent interest.
Cite as

Avi Kadria and Liam Roditty. New Approximate Distance Oracles and Their Applications. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 43:1-43:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kadria_et_al:LIPIcs.ISAAC.2025.43,
  author =	{Kadria, Avi and Roditty, Liam},
  title =	{{New Approximate Distance Oracles and Their Applications}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{43:1--43:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.43},
  URN =		{urn:nbn:de:0030-drops-249514},
  doi =		{10.4230/LIPIcs.ISAAC.2025.43},
  annote =	{Keywords: Distance oracles, Fine-grained algorithms, Graph algorithms, Data structures}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.DISC.2025.55
Brief Announcement: Concurrent Double-Ended Priority Queues

Authors: Panagiota Fatourou, Eric Ruppert, and Ioannis Xiradakis

Published in: LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025)

Abstract
This work provides the first concurrent implementation of a double-ended priority queue (DEPQ). We describe a general way to add an ExtractMax operation to any concurrent priority queue that already supports Insert and ExtractMin.
Cite as

Panagiota Fatourou, Eric Ruppert, and Ioannis Xiradakis. Brief Announcement: Concurrent Double-Ended Priority Queues. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 55:1-55:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{fatourou_et_al:LIPIcs.DISC.2025.55,
  author =	{Fatourou, Panagiota and Ruppert, Eric and Xiradakis, Ioannis},
  title =	{{Brief Announcement: Concurrent Double-Ended Priority Queues}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{55:1--55:7},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.55},
  URN =		{urn:nbn:de:0030-drops-248719},
  doi =		{10.4230/LIPIcs.DISC.2025.55},
  annote =	{Keywords: shared-memory, data structure, double-ended, priority queue, priority deque, heap, skip list, combining}
}
Document
DOI: 10.4230/LIPIcs.AFT.2025.20
Selfish Mining Under General Stochastic Rewards

Authors: Maryam Bahrani, Michael Neuder, and S. Matthew Weinberg

Published in: LIPIcs, Volume 354, 7th Conference on Advances in Financial Technologies (AFT 2025)

Abstract
Selfish miners selectively withhold blocks to earn disproportionately high revenue. The vast majority of the selfish mining literature focuses exclusively on block rewards. [Carlsten et al., 2016] is a notable exception, observing that similar strategic behavior is profitable in a zero-block-reward regime (the endgame for Bitcoin’s quadrennial halving schedule) if miners are compensated with transaction fees alone. Neither model fully captures miner incentives today. The block reward remains 3.125 BTC, yet some blocks yield significantly higher revenue. For example, congestion during the launch of the Babylon protocol in August 2024 caused transaction fees to spike from 0.14 BTC to 9.52 BTC, a 68× increase in fees within two blocks. Our results are both practical and theoretical. Of practical interest, we study selfish mining profitability under a combined reward function that more accurately models miner incentives. This analysis enables us to make quantitative claims about protocol risk (e.g., the mining power at which a selfish strategy becomes profitable is reduced by 22% when optimizing over the combined reward function versus block rewards alone) and qualitative observations (e.g., a miner considering both block rewards and transaction fees will mine more or less aggressively respectively than if they cared about either alone). These practical results follow from our novel model and methodology, which constitute our theoretical contributions. We model general, time-accruing stochastic rewards in the Nakamoto Consensus Game, which requires explicit treatment of difficult adjustment and randomness; we characterize reward function structure through a set of properties (e.g., that rewards accrue only as a function of time since the parent block). We present a new methodology to analytically calculate expected selfish miner rewards under a broad class of stochastic reward functions and validate our method numerically by comparing it with the existing literature and simulating the combined reward sources directly.
Cite as

Maryam Bahrani, Michael Neuder, and S. Matthew Weinberg. Selfish Mining Under General Stochastic Rewards. In 7th Conference on Advances in Financial Technologies (AFT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 354, pp. 20:1-20:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bahrani_et_al:LIPIcs.AFT.2025.20,
  author =	{Bahrani, Maryam and Neuder, Michael and Weinberg, S. Matthew},
  title =	{{Selfish Mining Under General Stochastic Rewards}},
  booktitle =	{7th Conference on Advances in Financial Technologies (AFT 2025)},
  pages =	{20:1--20:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-400-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{354},
  editor =	{Avarikioti, Zeta and Christin, Nicolas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AFT.2025.20},
  URN =		{urn:nbn:de:0030-drops-247396},
  doi =		{10.4230/LIPIcs.AFT.2025.20},
  annote =	{Keywords: Proof-of-Work, Selfish Mining, MEV}
}
Document
DOI: 10.4230/LIPIcs.CCC.2025.30
Online Condensing of Unpredictable Sources via Random Walks

Authors: Dean Doron, Dana Moshkovitz, Justin Oh, and David Zuckerman

Published in: LIPIcs, Volume 339, 40th Computational Complexity Conference (CCC 2025)

Abstract
A natural model of a source of randomness consists of a long stream of symbols X = X_1∘…∘X_t, with some guarantee on the entropy of X_i conditioned on the outcome of the prefix x_1,… ,x_{i-1}. We study unpredictable sources, a generalization of the almost Chor-Goldreich (CG) sources considered in [Doron et al., 2023]. In an unpredictable source X, for a typical draw of x ∼ X, for most i-s, the element x_i has a low probability of occurring given x_1,… ,x_{i-1}. Such a model relaxes the often unrealistic assumption of a CG source that for every i, and every x_1,… ,x_{i-1}, the next symbol X_i has sufficiently large entropy. Unpredictable sources subsume all previously considered notions of almost CG sources, including notions that [Doron et al., 2023] failed to analyze, and including those that are equivalent to general sources with high min entropy. For a lossless expander G = (V,E) with m = log |V|, we consider a random walk V_0,V_1,…,V_t on G using unpredictable instructions that have sufficient entropy with respect to m. Our main theorem is that for almost all the steps t/2 ≤ i ≤ t in the walk, the vertex V_i is close to a distribution with min-entropy at least m-O(1). As a result, we obtain seeded online condensers with constant entropy gap, and seedless (deterministic) condensers outputting a constant fraction of the entropy. In particular, our condensers run in space comparable to the output entropy, as opposed to the size of the stream, and even when the length t of the stream is not known ahead of time. As another corollary, we obtain a new extractor based on expander random walks handling lower entropy than the classic expander based construction relying on spectral techniques [Gillman, 1998]. As our main technical tool, we provide a novel analysis covering a key case of adversarial random walks on lossless expanders that [Doron et al., 2023] fails to address. As part of the analysis, we provide a "chain rule for vertex probabilities". The standard chain rule states that for every x ∼ X and i, Pr(x_1,… ,x_i) = Pr[X_i = x_i|X_[1,i-1] = x_1,… ,x_{i-1}] ⋅ Pr(x_1,… ,x_{i-1}). If W(x₁,… ,x_i) is the vertex reached using x₁,… ,x_i, then the chain rule for vertex probabilities essentially states that the same phenomena occurs for a typical x: Pr [V_i = W(x_1,… ,x_i)] ≲ Pr[X_i = x_i|X_[1,i-1] = x_1,… ,x_{i-1}] ⋅ Pr[V_{i-1} = W(x_1,… ,x_{i-1})], where V_i is the vertex distribution of the random walk at step i using X.
Cite as

Dean Doron, Dana Moshkovitz, Justin Oh, and David Zuckerman. Online Condensing of Unpredictable Sources via Random Walks. In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 30:1-30:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{doron_et_al:LIPIcs.CCC.2025.30,
  author =	{Doron, Dean and Moshkovitz, Dana and Oh, Justin and Zuckerman, David},
  title =	{{Online Condensing of Unpredictable Sources via Random Walks}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{30:1--30:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-379-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{339},
  editor =	{Srinivasan, Srikanth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2025.30},
  URN =		{urn:nbn:de:0030-drops-237243},
  doi =		{10.4230/LIPIcs.CCC.2025.30},
  annote =	{Keywords: Randomness Extractors, Expander Graphs}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.48
Improved Streaming Edge Coloring

Authors: Shiri Chechik, Hongyi Chen, and Tianyi Zhang

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
Given a graph, an edge coloring assigns colors to edges so that no pairs of adjacent edges share the same color. We are interested in edge coloring algorithms under the W-streaming model. In this model, the algorithm does not have enough memory to hold the entire graph, so the edges of the input graph are read from a data stream one by one in an unknown order, and the algorithm needs to print a valid edge coloring in an output stream. The performance of the algorithm is measured by the amount of space and the number of different colors it uses. This streaming edge coloring problem has been studied by several works in recent years. When the input graph contains n vertices and has maximum vertex degree Δ, it is known that in the W-streaming model, an O(Δ²)-edge coloring can be computed deterministically with Õ(n) space [Ansari, Saneian, and Zarrabi-Zadeh, 2022], or an O(Δ^{1.5})-edge coloring can be computed by a Õ(n)-space randomized algorithm [Behnezhad, Saneian, 2024] [Chechik, Mukhtar, Zhang, 2024]. In this paper, we achieve polynomial improvement over previous results. Specifically, we show how to improve the number of colors to Õ(Δ^{4/3+ε}) using space Õ(n) deterministically, for any constant ε > 0. This is the first deterministic result that bypasses the quadratic bound on the number of colors while using near-linear space.
Cite as

Shiri Chechik, Hongyi Chen, and Tianyi Zhang. Improved Streaming Edge Coloring. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 48:1-48:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chechik_et_al:LIPIcs.ICALP.2025.48,
  author =	{Chechik, Shiri and Chen, Hongyi and Zhang, Tianyi},
  title =	{{Improved Streaming Edge Coloring}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{48:1--48:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.48},
  URN =		{urn:nbn:de:0030-drops-234257},
  doi =		{10.4230/LIPIcs.ICALP.2025.48},
  annote =	{Keywords: edge coloring, streaming}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.40
Derandomized Squaring: An Analytical Insight into Its True Behavior

Authors: Gil Cohen, Itay Cohen, Gal Maor, and Yuval Peled

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract
The notion of the derandomized square of two graphs, denoted as G s H, was introduced by Rozenman and Vadhan as they rederived Reingold’s Theorem, SL = 𝐋. This pseudorandom primitive, closely related to the Zig-Zag product, plays a crucial role in recent advancements on space-bounded derandomization. For this and other reasons, understanding the spectral expansion λ(G s H) becomes paramount. Rozenman and Vadhan derived an upper bound for λ(G s H) in terms of the spectral expansions of the individual graphs, λ(G) and λ(H). They also proved their bound is optimal if the only information incorporated to the bound is the spectral expansion of the two graphs. The objective of this work is to gain deeper insights into the behavior of derandomized squaring by taking into account the entire spectrum of H, where we focus on a vertex-transitive c-regular H. Utilizing deep results from analytic combinatorics, we establish a lower bound on λ(G s H) that applies universally to all graphs G. Our work reveals that the bound is the minimum value of the function d⋅ x - d(d-1)χ_x(H)/χ_x'(H) in the domain (c,∞), where χ_x(H) is the characteristic polynomial of the d-vertex graph H. This bound lies far below the known upper bound for λ(G s H) for most reasonable choices for H. Empirical evidence suggests that our lower bound is optimal. We support the tightness of our lower bound by showing that the bound is tight for a class of graphs which exhibit local behavior similar to a derandomized squaring operation with H. To this end, we make use of finite free probability theory. In our second result, we resolve an open question posed by Cohen and Maor (STOC 2023) and establish a lower bound for the spectral expansion of rotating expanders. These graphs are constructed by taking a random walk with vertex permutations occurring after each step. We prove that Cohen and Maor’s construction is essentially optimal. Unlike our results on derandomized squaring, the proof in this instance relies solely on combinatorial methods. The key insight lies in establishing a connection between random walks on graph products and the Fuss-Catalan numbers.
Cite as

Gil Cohen, Itay Cohen, Gal Maor, and Yuval Peled. Derandomized Squaring: An Analytical Insight into Its True Behavior. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 40:1-40:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cohen_et_al:LIPIcs.ITCS.2025.40,
  author =	{Cohen, Gil and Cohen, Itay and Maor, Gal and Peled, Yuval},
  title =	{{Derandomized Squaring: An Analytical Insight into Its True Behavior}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{40:1--40:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.40},
  URN =		{urn:nbn:de:0030-drops-226681},
  doi =		{10.4230/LIPIcs.ITCS.2025.40},
  annote =	{Keywords: Derandomized Squaring, Spectral Graph Theory, Analytic Combinatorics}
}
Document
DOI: 10.4230/LIPIcs.CCC.2023.8
Spectral Expanding Expanders

Authors: Gil Cohen and Itay Cohen

Published in: LIPIcs, Volume 264, 38th Computational Complexity Conference (CCC 2023)

Abstract
Dinitz, Schapira, and Valadarsky [Dinitz et al., 2017] introduced the intriguing notion of expanding expanders - a family of expander graphs with the property that every two consecutive graphs in the family differ only on a small number of edges. Such a family allows one to add and remove vertices with only few edge updates, making them useful in dynamic settings such as for datacenter network topologies and for the design of distributed algorithms for self-healing expanders. [Dinitz et al., 2017] constructed explicit expanding-expanders based on the Bilu-Linial construction of spectral expanders [Bilu and Linial, 2006]. The construction of expanding expanders, however, ends up being of edge expanders, thus, an open problem raised by [Dinitz et al., 2017] is to construct spectral expanding expanders (SEE). In this work, we resolve this question by constructing SEE with spectral expansion which, like [Bilu and Linial, 2006], is optimal up to a poly-logarithmic factor, and the number of edge updates is optimal up to a constant. We further give a simple proof for the existence of SEE that are close to Ramanujan up to a small additive term. As in [Dinitz et al., 2017], our construction is based on interpolating between a graph and its lift. However, to establish spectral expansion, we carefully weigh the interpolated graphs, dubbed partial lifts, in a way that enables us to conduct a delicate analysis of their spectrum. In particular, at a crucial point in the analysis, we consider the eigenvectors structure of the partial lifts.
Cite as

Gil Cohen and Itay Cohen. Spectral Expanding Expanders. In 38th Computational Complexity Conference (CCC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 264, pp. 8:1-8:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{cohen_et_al:LIPIcs.CCC.2023.8,
  author =	{Cohen, Gil and Cohen, Itay},
  title =	{{Spectral Expanding Expanders}},
  booktitle =	{38th Computational Complexity Conference (CCC 2023)},
  pages =	{8:1--8:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-282-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{264},
  editor =	{Ta-Shma, Amnon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2023.8},
  URN =		{urn:nbn:de:0030-drops-182780},
  doi =		{10.4230/LIPIcs.CCC.2023.8},
  annote =	{Keywords: Expanders, Normalized Random Walk, Spectral Analysis}
}
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