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Documents authored by Weinberg, S. Matthew

Document
DOI: 10.4230/LIPIcs.AFT.2024.10
Optimal RANDAO Manipulation in Ethereum

Authors: Kaya Alpturer and S. Matthew Weinberg

Published in: LIPIcs, Volume 316, 6th Conference on Advances in Financial Technologies (AFT 2024)

Abstract
It is well-known that RANDAO manipulation is possible in Ethereum if an adversary controls the proposers assigned to the last slots in an epoch. We provide a methodology to compute, for any fraction α of stake owned by an adversary, the maximum fraction f(α) of rounds that a strategic adversary can propose. We further implement our methodology and compute f(⋅) for all α. For example, we conclude that an optimal strategic participant with 5% of the stake can propose a 5.048% fraction of rounds, 10% of the stake can propose a 10.19% fraction of rounds, and 20% of the stake can propose a 20.68% fraction of rounds.
Cite as

Kaya Alpturer and S. Matthew Weinberg. Optimal RANDAO Manipulation in Ethereum. In 6th Conference on Advances in Financial Technologies (AFT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 316, pp. 10:1-10:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{alpturer_et_al:LIPIcs.AFT.2024.10,
  author =	{Alpturer, Kaya and Weinberg, S. Matthew},
  title =	{{Optimal RANDAO Manipulation in Ethereum}},
  booktitle =	{6th Conference on Advances in Financial Technologies (AFT 2024)},
  pages =	{10:1--10:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-345-4},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{316},
  editor =	{B\"{o}hme, Rainer and Kiffer, Lucianna},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AFT.2024.10},
  URN =		{urn:nbn:de:0030-drops-209467},
  doi =		{10.4230/LIPIcs.AFT.2024.10},
  annote =	{Keywords: Proof of Stake, Consensus, Blockchain, Ethereum, Randomness manipulation}
}
Document
DOI: 10.4230/LIPIcs.AFT.2024.30
Profitable Manipulations of Cryptographic Self-Selection Are Statistically Detectable

Authors: Linda Cai, Jingyi Liu, S. Matthew Weinberg, and Chenghan Zhou

Published in: LIPIcs, Volume 316, 6th Conference on Advances in Financial Technologies (AFT 2024)

Abstract
Cryptographic Self-Selection is a common primitive underlying leader-selection for Proof-of-Stake blockchain protocols. The concept was first popularized in Algorand [Jing Chen and Silvio Micali, 2019], who also observed that the protocol might be manipulable. [Matheus V. X. Ferreira et al., 2022] provide a concrete manipulation that is strictly profitable for a staker of any size (and also prove upper bounds on the gains from manipulation). Separately, [Maryam Bahrani and S. Matthew Weinberg, 2024; Aviv Yaish et al., 2023] initiate the study of undetectable profitable manipulations of consensus protocols with a focus on the seminal Selfish Mining strategy [Eyal and Sirer, 2014] for Bitcoin’s Proof-of-Work longest-chain protocol. They design a Selfish Mining variant that, for sufficiently large miners, is strictly profitable yet also indistinguishable to an onlooker from routine latency (that is, a sufficiently large profit-maximizing miner could use their strategy to strictly profit over being honest in a way that still appears to the rest of the network as though everyone is honest but experiencing mildly higher latency. This avoids any risk of negatively impacting the value of the underlying cryptocurrency due to attack detection). We investigate the detectability of profitable manipulations of the canonical cryptographic self-selection leader selection protocol introduced in [Jing Chen and Silvio Micali, 2019] and studied in [Matheus V. X. Ferreira et al., 2022], and establish that for any player with α < (3-√5)/2 ≈ 0.38 fraction of the total stake, every strictly profitable manipulation is statistically detectable. Specifically, we consider an onlooker who sees only the random seed of each round (and does not need to see any other broadcasts by any other players). We show that the distribution of the sequence of random seeds when any player is profitably manipulating the protocol is inconsistent with any distribution that could arise by honest stakers being offline or timing out (for a natural stylized model of honest timeouts).
Cite as

Linda Cai, Jingyi Liu, S. Matthew Weinberg, and Chenghan Zhou. Profitable Manipulations of Cryptographic Self-Selection Are Statistically Detectable. In 6th Conference on Advances in Financial Technologies (AFT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 316, pp. 30:1-30:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{cai_et_al:LIPIcs.AFT.2024.30,
  author =	{Cai, Linda and Liu, Jingyi and Weinberg, S. Matthew and Zhou, Chenghan},
  title =	{{Profitable Manipulations of Cryptographic Self-Selection Are Statistically Detectable}},
  booktitle =	{6th Conference on Advances in Financial Technologies (AFT 2024)},
  pages =	{30:1--30:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-345-4},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{316},
  editor =	{B\"{o}hme, Rainer and Kiffer, Lucianna},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AFT.2024.30},
  URN =		{urn:nbn:de:0030-drops-209660},
  doi =		{10.4230/LIPIcs.AFT.2024.30},
  annote =	{Keywords: Blockchain, Cryptocurrency, Proof-of-Stake, Strategic Mining, Statistical Detection}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.115
On the Cut-Query Complexity of Approximating Max-Cut

Authors: Orestis Plevrakis, Seyoon Ragavan, and S. Matthew Weinberg

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
We consider the problem of query-efficient global max-cut on a weighted undirected graph in the value oracle model examined by [Rubinstein et al., 2018]. Graph algorithms in this cut query model and other query models have recently been studied for various other problems such as min-cut, connectivity, bipartiteness, and triangle detection. Max-cut in the cut query model can also be viewed as a natural special case of submodular function maximization: on query S ⊆ V, the oracle returns the total weight of the cut between S and V\S. Our first main technical result is a lower bound stating that a deterministic algorithm achieving a c-approximation for any c > 1/2 requires Ω(n) queries. This uses an extension of the cut dimension to rule out approximation (prior work of [Graur et al., 2020] introducing the cut dimension only rules out exact solutions). Secondly, we provide a randomized algorithm with Õ(n) queries that finds a c-approximation for any c < 1. We achieve this using a query-efficient sparsifier for undirected weighted graphs (prior work of [Rubinstein et al., 2018] holds only for unweighted graphs). To complement these results, for most constants c ∈ (0,1], we nail down the query complexity of achieving a c-approximation, for both deterministic and randomized algorithms (up to logarithmic factors). Analogously to general submodular function maximization in the same model, we observe a phase transition at c = 1/2: we design a deterministic algorithm for global c-approximate max-cut in O(log n) queries for any c < 1/2, and show that any randomized algorithm requires Ω(n/log n) queries to find a c-approximate max-cut for any c > 1/2. Additionally, we show that any deterministic algorithm requires Ω(n²) queries to find an exact max-cut (enough to learn the entire graph).
Cite as

Orestis Plevrakis, Seyoon Ragavan, and S. Matthew Weinberg. On the Cut-Query Complexity of Approximating Max-Cut. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 115:1-115:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{plevrakis_et_al:LIPIcs.ICALP.2024.115,
  author =	{Plevrakis, Orestis and Ragavan, Seyoon and Weinberg, S. Matthew},
  title =	{{On the Cut-Query Complexity of Approximating Max-Cut}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{115:1--115:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.115},
  URN =		{urn:nbn:de:0030-drops-202587},
  doi =		{10.4230/LIPIcs.ICALP.2024.115},
  annote =	{Keywords: query complexity, maximum cut, approximation algorithms, graph sparsification}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2024.39
Simple and Optimal Online Contention Resolution Schemes for k-Uniform Matroids

Authors: Atanas Dinev and S. Matthew Weinberg

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)

Abstract
We provide a simple (1-O(1/(√{k)}))-selectable Online Contention Resolution Scheme for k-uniform matroids against a fixed-order adversary. If A_i and G_i denote the set of selected elements and the set of realized active elements among the first i (respectively), our algorithm selects with probability 1-1/(√{k)} any active element i such that |A_{i-1}| + 1 ≤ (1-1/(√{k)})⋅ 𝔼[|G_i|]+√k. This implies a (1-O(1/(√{k)})) prophet inequality against fixed-order adversaries for k-uniform matroids that is considerably simpler than previous algorithms [Alaei, 2014; Azar et al., 2014; Jiang et al., 2022]. We also prove that no OCRS can be (1-Ω(√{(log k)/k}))-selectable for k-uniform matroids against an almighty adversary. This guarantee is matched by the (known) simple greedy algorithm that selects every active element with probability 1-Θ(√{(log k)/k}) [Hajiaghayi et al., 2007].
Cite as

Atanas Dinev and S. Matthew Weinberg. Simple and Optimal Online Contention Resolution Schemes for k-Uniform Matroids. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 39:1-39:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{dinev_et_al:LIPIcs.ITCS.2024.39,
  author =	{Dinev, Atanas and Weinberg, S. Matthew},
  title =	{{Simple and Optimal Online Contention Resolution Schemes for k-Uniform Matroids}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{39:1--39:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.39},
  URN =		{urn:nbn:de:0030-drops-195677},
  doi =		{10.4230/LIPIcs.ITCS.2024.39},
  annote =	{Keywords: online contention resolutions schemes, prophet inequalities, online algorithms, approximation algorithms}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.AFT.2023
LIPIcs, Volume 282, AFT 2023, Complete Volume

Authors: Joseph Bonneau and S. Matthew Weinberg

Published in: LIPIcs, Volume 282, 5th Conference on Advances in Financial Technologies (AFT 2023)

Abstract
LIPIcs, Volume 282, AFT 2023, Complete Volume
Cite as

5th Conference on Advances in Financial Technologies (AFT 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 282, pp. 1-718, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@Proceedings{bonneau_et_al:LIPIcs.AFT.2023,
  title =	{{LIPIcs, Volume 282, AFT 2023, Complete Volume}},
  booktitle =	{5th Conference on Advances in Financial Technologies (AFT 2023)},
  pages =	{1--718},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-303-4},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{282},
  editor =	{Bonneau, Joseph and Weinberg, S. Matthew},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AFT.2023},
  URN =		{urn:nbn:de:0030-drops-191884},
  doi =		{10.4230/LIPIcs.AFT.2023},
  annote =	{Keywords: LIPIcs, Volume 282, AFT 2023, Complete Volume}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.AFT.2023.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Joseph Bonneau and S. Matthew Weinberg

Published in: LIPIcs, Volume 282, 5th Conference on Advances in Financial Technologies (AFT 2023)

Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as

5th Conference on Advances in Financial Technologies (AFT 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 282, pp. 0:i-0:xx, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{bonneau_et_al:LIPIcs.AFT.2023.0,
  author =	{Bonneau, Joseph and Weinberg, S. Matthew},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{5th Conference on Advances in Financial Technologies (AFT 2023)},
  pages =	{0:i--0:xx},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-303-4},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{282},
  editor =	{Bonneau, Joseph and Weinberg, S. Matthew},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AFT.2023.0},
  URN =		{urn:nbn:de:0030-drops-191894},
  doi =		{10.4230/LIPIcs.AFT.2023.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2023.95
An Improved Lower Bound for Matroid Intersection Prophet Inequalities

Authors: Raghuvansh R. Saxena, Santhoshini Velusamy, and S. Matthew Weinberg

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)

Abstract
We consider prophet inequalities subject to feasibility constraints that are the intersection of q matroids. The best-known algorithms achieve a Θ(q)-approximation, even when restricted to instances that are the intersection of q partition matroids, and with i.i.d. Bernoulli random variables [José R. Correa et al., 2022; Moran Feldman et al., 2016; Marek Adamczyk and Michal Wlodarczyk, 2018]. The previous best-known lower bound is Θ(√q) due to a simple construction of [Robert Kleinberg and S. Matthew Weinberg, 2012] (which uses i.i.d. Bernoulli random variables, and writes the construction as the intersection of partition matroids). We establish an improved lower bound of q^{1/2+Ω(1/log log q)} by writing the construction of [Robert Kleinberg and S. Matthew Weinberg, 2012] as the intersection of asymptotically fewer partition matroids. We accomplish this via an improved upper bound on the product dimension of a graph with p^p disjoint cliques of size p, using recent techniques developed in [Noga Alon and Ryan Alweiss, 2020].
Cite as

Raghuvansh R. Saxena, Santhoshini Velusamy, and S. Matthew Weinberg. An Improved Lower Bound for Matroid Intersection Prophet Inequalities. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 95:1-95:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{saxena_et_al:LIPIcs.ITCS.2023.95,
  author =	{Saxena, Raghuvansh R. and Velusamy, Santhoshini and Weinberg, S. Matthew},
  title =	{{An Improved Lower Bound for Matroid Intersection Prophet Inequalities}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{95:1--95:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.95},
  URN =		{urn:nbn:de:0030-drops-175986},
  doi =		{10.4230/LIPIcs.ITCS.2023.95},
  annote =	{Keywords: Prophet Inequalities, Intersection of Matroids}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2022.66
Credible, Strategyproof, Optimal, and Bounded Expected-Round Single-Item Auctions for All Distributions

Authors: Meryem Essaidi, Matheus V. X. Ferreira, and S. Matthew Weinberg

Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)

Abstract
We consider a revenue-maximizing seller with a single item for sale to multiple buyers with independent and identically distributed valuations. Akbarpour and Li (2020) show that the only optimal, credible, strategyproof auction is the ascending price auction with reserves which has unbounded communication complexity. Recent work of Ferreira and Weinberg (2020) circumvents their impossibility result assuming the existence of cryptographically secure commitment schemes, and designs a two-round credible, strategyproof, optimal auction. However, their auction is only credible when buyers' valuations are MHR or α-strongly regular: they show their auction might not be credible even when there is a single buyer drawn from a non-MHR distribution. In this work, under the same cryptographic assumptions, we identify a new single-item auction that is credible, strategyproof, revenue optimal, and terminates in constant rounds in expectation for all distributions with finite monopoly price.
Cite as

Meryem Essaidi, Matheus V. X. Ferreira, and S. Matthew Weinberg. Credible, Strategyproof, Optimal, and Bounded Expected-Round Single-Item Auctions for All Distributions. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 66:1-66:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{essaidi_et_al:LIPIcs.ITCS.2022.66,
  author =	{Essaidi, Meryem and Ferreira, Matheus V. X. and Weinberg, S. Matthew},
  title =	{{Credible, Strategyproof, Optimal, and Bounded Expected-Round Single-Item Auctions for All Distributions}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{66:1--66:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.66},
  URN =		{urn:nbn:de:0030-drops-156621},
  doi =		{10.4230/LIPIcs.ITCS.2022.66},
  annote =	{Keywords: Credible Auctions, Cryptographically Secure, Single-Item}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2021.14
Approximately Strategyproof Tournament Rules in the Probabilistic Setting

Authors: Kimberly Ding and S. Matthew Weinberg

Published in: LIPIcs, Volume 185, 12th Innovations in Theoretical Computer Science Conference (ITCS 2021)

Abstract
We consider the manipulability of tournament rules which map the results of binom(n,2) pairwise matches and select a winner. Prior work designs simple tournament rules such that no pair of teams can manipulate the outcome of their match to improve their probability of winning by more than 1/3, and this is the best possible among any Condorcet-consistent tournament rule (which selects an undefeated team whenever one exists) [Jon Schneider et al., 2017; Ariel Schvartzman et al., 2020]. These lower bounds require the manipulators to know precisely the outcome of all future matches. We take a beyond worst-case view and instead consider tournaments which are "close to uniform": the outcome of all matches are independent, and no team is believed to win any match with probability exceeding 1/2+ε. We show that Randomized Single Elimination Bracket [Jon Schneider et al., 2017] and a new tournament rule we term Randomized Death Match have the property that no pair of teams can manipulate the outcome of their match to improve their probability of winning by more than ε/3 + 2ε²/3, for all ε, and this is the best possible among any Condorcet-consistent tournament rule. Our main technical contribution is a recursive framework to analyze the manipulability of certain forms of tournament rules. In addition to our main results, this view helps streamline previous analysis of Randomized Single Elimination Bracket, and may be of independent interest.
Cite as

Kimberly Ding and S. Matthew Weinberg. Approximately Strategyproof Tournament Rules in the Probabilistic Setting. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 14:1-14:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{ding_et_al:LIPIcs.ITCS.2021.14,
  author =	{Ding, Kimberly and Weinberg, S. Matthew},
  title =	{{Approximately Strategyproof Tournament Rules in the Probabilistic Setting}},
  booktitle =	{12th Innovations in Theoretical Computer Science Conference (ITCS 2021)},
  pages =	{14:1--14:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-177-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{185},
  editor =	{Lee, James R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2021.14},
  URN =		{urn:nbn:de:0030-drops-135532},
  doi =		{10.4230/LIPIcs.ITCS.2021.14},
  annote =	{Keywords: Tournaments, Incentive Compatibility, Recursive Analysis, Social Choice Theory}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2020.8
Asynchronous Majority Dynamics in Preferential Attachment Trees

Authors: Maryam Bahrani, Nicole Immorlica, Divyarthi Mohan, and S. Matthew Weinberg

Published in: LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

Abstract
We study information aggregation in networks where agents make binary decisions (labeled incorrect or correct). Agents initially form independent private beliefs about the better decision, which is correct with probability 1/2+δ. The dynamics we consider are asynchronous (each round, a single agent updates their announced decision) and non-Bayesian (agents simply copy the majority announcements among their neighbors, tie-breaking in favor of their private signal). Our main result proves that when the network is a tree formed according to the preferential attachment model [Barabási and Albert, 1999], with high probability, the process stabilizes in a correct majority within O(n log n/log log n) rounds. We extend our results to other tree structures, including balanced M-ary trees for any M.
Cite as

Maryam Bahrani, Nicole Immorlica, Divyarthi Mohan, and S. Matthew Weinberg. Asynchronous Majority Dynamics in Preferential Attachment Trees. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 8:1-8:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{bahrani_et_al:LIPIcs.ICALP.2020.8,
  author =	{Bahrani, Maryam and Immorlica, Nicole and Mohan, Divyarthi and Weinberg, S. Matthew},
  title =	{{Asynchronous Majority Dynamics in Preferential Attachment Trees}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{8:1--8:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.8},
  URN =		{urn:nbn:de:0030-drops-124156},
  doi =		{10.4230/LIPIcs.ICALP.2020.8},
  annote =	{Keywords: Opinion Dynamics, Information Cascades, Preferential Attachment, Majority Dynamics, non-Bayesian Asynchronous Learning, Stochastic Processes}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2020.3
Approximately Strategyproof Tournament Rules: On Large Manipulating Sets and Cover-Consistence

Authors: Ariel Schvartzman, S. Matthew Weinberg, Eitan Zlatin, and Albert Zuo

Published in: LIPIcs, Volume 151, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)

Abstract
We consider the manipulability of tournament rules, in which n teams play a round robin tournament and a winner is (possibly randomly) selected based on the outcome of all binom{n}{2} matches. Prior work defines a tournament rule to be k-SNM-α if no set of ≤ k teams can fix the ≤ binom{k}{2} matches among them to increase their probability of winning by >α and asks: for each k, what is the minimum α(k) such that a Condorcet-consistent (i.e. always selects a Condorcet winner when one exists) k-SNM-α(k) tournament rule exists? A simple example witnesses that α(k) ≥ (k-1)/(2k-1) for all k, and [Jon Schneider et al., 2017] conjectures that this is tight (and prove it is tight for k=2). Our first result refutes this conjecture: there exists a sufficiently large k such that no Condorcet-consistent tournament rule is k-SNM-1/2. Our second result leverages similar machinery to design a new tournament rule which is k-SNM-2/3 for all k (and this is the first tournament rule which is k-SNM-(<1) for all k). Our final result extends prior work, which proves that single-elimination bracket with random seeding is 2-SNM-1/3 [Jon Schneider et al., 2017], in a different direction by seeking a stronger notion of fairness than Condorcet-consistence. We design a new tournament rule, which we call Randomized-King-of-the-Hill, which is 2-SNM-1/3 and cover-consistent (the winner is an uncovered team with probability 1).
Cite as

Ariel Schvartzman, S. Matthew Weinberg, Eitan Zlatin, and Albert Zuo. Approximately Strategyproof Tournament Rules: On Large Manipulating Sets and Cover-Consistence. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 3:1-3:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{schvartzman_et_al:LIPIcs.ITCS.2020.3,
  author =	{Schvartzman, Ariel and Weinberg, S. Matthew and Zlatin, Eitan and Zuo, Albert},
  title =	{{Approximately Strategyproof Tournament Rules: On Large Manipulating Sets and Cover-Consistence}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{3:1--3:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Vidick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.3},
  URN =		{urn:nbn:de:0030-drops-116881},
  doi =		{10.4230/LIPIcs.ITCS.2020.3},
  annote =	{Keywords: Tournament design, Non-manipulability, Cover-consistence, Strategyproofness}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2020.60
Optimal Single-Choice Prophet Inequalities from Samples

Authors: Aviad Rubinstein, Jack Z. Wang, and S. Matthew Weinberg

Published in: LIPIcs, Volume 151, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)

Abstract
We study the single-choice Prophet Inequality problem when the gambler is given access to samples. We show that the optimal competitive ratio of 1/2 can be achieved with a single sample from each distribution. When the distributions are identical, we show that for any constant ε > 0, O(n) samples from the distribution suffice to achieve the optimal competitive ratio (≈ 0.745) within (1+ε), resolving an open problem of [José R. Correa et al., 2019].
Cite as

Aviad Rubinstein, Jack Z. Wang, and S. Matthew Weinberg. Optimal Single-Choice Prophet Inequalities from Samples. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 60:1-60:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{rubinstein_et_al:LIPIcs.ITCS.2020.60,
  author =	{Rubinstein, Aviad and Wang, Jack Z. and Weinberg, S. Matthew},
  title =	{{Optimal Single-Choice Prophet Inequalities from Samples}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{60:1--60:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Vidick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.60},
  URN =		{urn:nbn:de:0030-drops-117452},
  doi =		{10.4230/LIPIcs.ITCS.2020.60},
  annote =	{Keywords: Online algorithms, Probability, Optimization, Prophet inequalities, Samples, Auctions}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2020.61
Implementation in Advised Strategies: Welfare Guarantees from Posted-Price Mechanisms When Demand Queries Are NP-Hard

Authors: Linda Cai, Clay Thomas, and S. Matthew Weinberg

Published in: LIPIcs, Volume 151, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)

Abstract
State-of-the-art posted-price mechanisms for submodular bidders with m items achieve approximation guarantees of O((log log m)^3) [Sepehr Assadi and Sahil Singla, 2019]. Their truthfulness, however, requires bidders to compute an NP-hard demand-query. Some computational complexity of this form is unavoidable, as it is NP-hard for truthful mechanisms to guarantee even an m^(1/2-ε)-approximation for any ε > 0 [Shahar Dobzinski and Jan Vondrák, 2016]. Together, these establish a stark distinction between computationally-efficient and communication-efficient truthful mechanisms. We show that this distinction disappears with a mild relaxation of truthfulness, which we term implementation in advised strategies. Specifically, advice maps a tentative strategy either to that same strategy itself, or one that dominates it. We say that a player follows advice as long as they never play actions which are dominated by advice. A poly-time mechanism guarantees an α-approximation in implementation in advised strategies if there exists advice (which runs in poly-time) for each player such that an α-approximation is achieved whenever all players follow advice. Using an appropriate bicriterion notion of approximate demand queries (which can be computed in poly-time), we establish that (a slight modification of) the [Sepehr Assadi and Sahil Singla, 2019] mechanism achieves the same O((log log m)^3)-approximation in implementation in advised strategies.
Cite as

Linda Cai, Clay Thomas, and S. Matthew Weinberg. Implementation in Advised Strategies: Welfare Guarantees from Posted-Price Mechanisms When Demand Queries Are NP-Hard. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 61:1-61:32, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{cai_et_al:LIPIcs.ITCS.2020.61,
  author =	{Cai, Linda and Thomas, Clay and Weinberg, S. Matthew},
  title =	{{Implementation in Advised Strategies: Welfare Guarantees from Posted-Price Mechanisms When Demand Queries Are NP-Hard}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{61:1--61:32},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Vidick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.61},
  URN =		{urn:nbn:de:0030-drops-117464},
  doi =		{10.4230/LIPIcs.ITCS.2020.61},
  annote =	{Keywords: Combinatorial auctions, Posted-Price mechanisms, Submodular valuations, Incentive compatible}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2020.64
New Query Lower Bounds for Submodular Function Minimization

Authors: Andrei Graur, Tristan Pollner, Vidhya Ramaswamy, and S. Matthew Weinberg

Published in: LIPIcs, Volume 151, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)

Abstract
We consider submodular function minimization in the oracle model: given black-box access to a submodular set function f:2^[n] → ℝ, find an element of arg min_S {f(S)} using as few queries to f(⋅) as possible. State-of-the-art algorithms succeed with Õ(n²) queries [Yin Tat Lee et al., 2015], yet the best-known lower bound has never been improved beyond n [Nicholas J. A. Harvey, 2008]. We provide a query lower bound of 2n for submodular function minimization, a 3n/2-2 query lower bound for the non-trivial minimizer of a symmetric submodular function, and a binom{n}{2} query lower bound for the non-trivial minimizer of an asymmetric submodular function. Our 3n/2-2 lower bound results from a connection between SFM lower bounds and a novel concept we term the cut dimension of a graph. Interestingly, this yields a 3n/2-2 cut-query lower bound for finding the global mincut in an undirected, weighted graph, but we also prove it cannot yield a lower bound better than n+1 for s-t mincut, even in a directed, weighted graph.
Cite as

Andrei Graur, Tristan Pollner, Vidhya Ramaswamy, and S. Matthew Weinberg. New Query Lower Bounds for Submodular Function Minimization. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 64:1-64:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{graur_et_al:LIPIcs.ITCS.2020.64,
  author =	{Graur, Andrei and Pollner, Tristan and Ramaswamy, Vidhya and Weinberg, S. Matthew},
  title =	{{New Query Lower Bounds for Submodular Function Minimization}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{64:1--64:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Vidick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.64},
  URN =		{urn:nbn:de:0030-drops-117493},
  doi =		{10.4230/LIPIcs.ITCS.2020.64},
  annote =	{Keywords: submodular functions, query lower bounds, min cut}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2019.5
Bitcoin: A Natural Oligopoly

Authors: Nick Arnosti and S. Matthew Weinberg

Published in: LIPIcs, Volume 124, 10th Innovations in Theoretical Computer Science Conference (ITCS 2019)

Abstract
Although Bitcoin was intended to be a decentralized digital currency, in practice, mining power is quite concentrated. This fact is a persistent source of concern for the Bitcoin community. We provide an explanation using a simple model to capture miners' incentives to invest in equipment. In our model, n miners compete for a prize of fixed size. Each miner chooses an investment q_i, incurring cost c_i q_i, and then receives reward (q_i^alpha)/(sum_j q_j^alpha), for some alpha >= 1. When c_i = c_j for all i,j, and alpha = 1, there is a unique equilibrium where all miners invest equally. However, we prove that under seemingly mild deviations from this model, equilibrium outcomes become drastically more centralized. In particular, - When costs are asymmetric, if miner i chooses to invest, then miner j has market share at least 1-c_j/c_i. That is, if miner j has costs that are (e.g.) 20% lower than those of miner i, then miner j must control at least 20% of the total mining power. - In the presence of economies of scale (alpha > 1), every market participant has a market share of at least 1-1/(alpha), implying that the market features at most alpha/(alpha - 1) miners in total. We discuss the implications of our results for the future design of cryptocurrencies. In particular, our work further motivates the study of protocols that minimize "orphaned" blocks, proof-of-stake protocols, and incentive compatible protocols.
Cite as

Nick Arnosti and S. Matthew Weinberg. Bitcoin: A Natural Oligopoly. In 10th Innovations in Theoretical Computer Science Conference (ITCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 124, p. 5:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{arnosti_et_al:LIPIcs.ITCS.2019.5,
  author =	{Arnosti, Nick and Weinberg, S. Matthew},
  title =	{{Bitcoin: A Natural Oligopoly}},
  booktitle =	{10th Innovations in Theoretical Computer Science Conference (ITCS 2019)},
  pages =	{5:1--5:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-095-8},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{124},
  editor =	{Blum, Avrim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2019.5},
  URN =		{urn:nbn:de:0030-drops-100989},
  doi =		{10.4230/LIPIcs.ITCS.2019.5},
  annote =	{Keywords: Bitcoin, Cryptocurrencies, Rent-Seeking Competition}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2018.39
Computing Exact Minimum Cuts Without Knowing the Graph

Authors: Aviad Rubinstein, Tselil Schramm, and S. Matthew Weinberg

Published in: LIPIcs, Volume 94, 9th Innovations in Theoretical Computer Science Conference (ITCS 2018)

Abstract
We give query-efficient algorithms for the global min-cut and the s-t cut problem in unweighted, undirected graphs. Our oracle model is inspired by the submodular function minimization problem: on query S \subset V, the oracle returns the size of the cut between S and V \ S. We provide algorithms computing an exact minimum $s$-$t$ cut in $G$ with ~{O}(n^{5/3}) queries, and computing an exact global minimum cut of G with only ~{O}(n) queries (while learning the graph requires ~{\Theta}(n^2) queries).
Cite as

Aviad Rubinstein, Tselil Schramm, and S. Matthew Weinberg. Computing Exact Minimum Cuts Without Knowing the Graph. In 9th Innovations in Theoretical Computer Science Conference (ITCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 94, pp. 39:1-39:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{rubinstein_et_al:LIPIcs.ITCS.2018.39,
  author =	{Rubinstein, Aviad and Schramm, Tselil and Weinberg, S. Matthew},
  title =	{{Computing Exact Minimum Cuts Without Knowing the Graph}},
  booktitle =	{9th Innovations in Theoretical Computer Science Conference (ITCS 2018)},
  pages =	{39:1--39:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-060-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{94},
  editor =	{Karlin, Anna R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2018.39},
  URN =		{urn:nbn:de:0030-drops-83168},
  doi =		{10.4230/LIPIcs.ITCS.2018.39},
  annote =	{Keywords: query complexity, minimum cut}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2017.35
Condorcet-Consistent and Approximately Strategyproof Tournament Rules

Authors: Jon Schneider, Ariel Schvartzman, and S. Matthew Weinberg

Published in: LIPIcs, Volume 67, 8th Innovations in Theoretical Computer Science Conference (ITCS 2017)

Abstract
We consider the manipulability of tournament rules for round-robin tournaments of n competitors. Specifically, n competitors are competing for a prize, and a tournament rule r maps the result of all n(n-1)/2 pairwise matches (called a tournament, T) to a distribution over winners. Rule r is Condorcet-consistent if whenever i wins all n-1 of her matches, r selects i with probability 1. We consider strategic manipulation of tournaments where player j might throw their match to player i in order to increase the likelihood that one of them wins the tournament. Regardless of the reason why j chooses to do this, the potential for manipulation exists as long as Pr[r(T) = i] increases by more than Pr[r(T) = j] decreases. Unfortunately, it is known that every Condorcet-consistent rule is manipulable. In this work, we address the question of how manipulable Condorcet-consistent rules must necessarily be - by trying to minimize the difference between the increase in Pr[r(T) = i] and decrease in Pr[r(T) = j] for any potential manipulating pair. We show that every Condorcet-consistent rule is in fact 1/3-manipulable, and that selecting a winner according to a random single elimination bracket is not alpha-manipulable for any alpha > 1/3. We also show that many previously studied tournament formats are all 1/2-manipulable, and the popular class of Copeland rules (any rule that selects a player with the most wins) are all in fact 1-manipulable, the worst possible. Finally, we consider extensions to match-fixing among sets of more than two players.
Cite as

Jon Schneider, Ariel Schvartzman, and S. Matthew Weinberg. Condorcet-Consistent and Approximately Strategyproof Tournament Rules. In 8th Innovations in Theoretical Computer Science Conference (ITCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 67, pp. 35:1-35:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{schneider_et_al:LIPIcs.ITCS.2017.35,
  author =	{Schneider, Jon and Schvartzman, Ariel and Weinberg, S. Matthew},
  title =	{{Condorcet-Consistent and Approximately Strategyproof Tournament Rules}},
  booktitle =	{8th Innovations in Theoretical Computer Science Conference (ITCS 2017)},
  pages =	{35:1--35:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-029-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{67},
  editor =	{Papadimitriou, Christos H.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2017.35},
  URN =		{urn:nbn:de:0030-drops-81605},
  doi =		{10.4230/LIPIcs.ITCS.2017.35},
  annote =	{Keywords: Tournament design, Non-manipulability, Condorcet-consistent, Strategyproofness}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2014.192
Reaching Consensus via Non-Bayesian Asynchronous Learning in Social Networks

Authors: Michal Feldman, Nicole Immorlica, Brendan Lucier, and S. Matthew Weinberg

Published in: LIPIcs, Volume 28, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)

Abstract
We study the outcomes of information aggregation in online social networks. Our main result is that networks with certain realistic structural properties avoid information cascades and enable a population to effectively aggregate information. In our model, each individual in a network holds a private, independent opinion about a product or idea, biased toward a ground truth. Individuals declare their opinions asynchronously, can observe the stated opinions of their neighbors, and are free to update their declarations over time. Supposing that individuals conform with the majority report of their neighbors, we ask whether the population will eventually arrive at consensus on the ground truth. We show that the answer depends on the network structure: there exist networks for which consensus is unlikely, or for which declarations converge on the incorrect opinion with positive probability. On the other hand, we prove that for networks that are sparse and expansive, the population will converge to the correct opinion with high probability.
Cite as

Michal Feldman, Nicole Immorlica, Brendan Lucier, and S. Matthew Weinberg. Reaching Consensus via Non-Bayesian Asynchronous Learning in Social Networks. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 28, pp. 192-208, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{feldman_et_al:LIPIcs.APPROX-RANDOM.2014.192,
  author =	{Feldman, Michal and Immorlica, Nicole and Lucier, Brendan and Weinberg, S. Matthew},
  title =	{{Reaching Consensus via Non-Bayesian Asynchronous Learning in Social Networks}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)},
  pages =	{192--208},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-74-3},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{28},
  editor =	{Jansen, Klaus and Rolim, Jos\'{e} and Devanur, Nikhil R. and Moore, Cristopher},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2014.192},
  URN =		{urn:nbn:de:0030-drops-46976},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2014.192},
  annote =	{Keywords: Information Cascades, Social Networks, non-Bayesian Asynchronous Learning, Expander Graphs, Stochastic Processes}
}
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