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**Published in:** LIPIcs, Volume 276, 29th International Conference on DNA Computing and Molecular Programming (DNA 29) (2023)

This paper studies the (discrete) chemical reaction network (CRN) computational model that emerged in the last two decades as an abstraction for molecular programming. The correctness of CRN protocols is typically established under one of two possible schedulers that determine how the execution advances: (1) a stochastic scheduler that obeys the (continuous time) Markov process dictated by the standard model of stochastic chemical kinetics; or (2) an adversarial scheduler whose only commitment is to maintain a certain fairness condition. The latter scheduler is justified by the fact that the former one crucially assumes "idealized conditions" that more often than not, do not hold in real wet-lab experiments. However, when it comes to analyzing the runtime of CRN protocols, the existing literature focuses strictly on the stochastic scheduler, thus raising the research question that drives this work: Is there a meaningful way to quantify the runtime of CRNs without the idealized conditions assumption?
The main conceptual contribution of the current paper is to answer this question in the affirmative, formulating a new runtime measure for CRN protocols that does not rely on idealized conditions. This runtime measure is based on an adapted (weaker) fairness condition as well as a novel scheme that enables partitioning the execution into short rounds and charging the runtime for each round individually (inspired by definitions for the runtime of asynchronous distributed algorithms). Following that, we turn to investigate various fundamental computational tasks and establish (often tight) bounds on the runtime of the corresponding CRN protocols operating under the adversarial scheduler. This includes an almost complete chart of the runtime complexity landscape of predicate decidability tasks.

Anne Condon, Yuval Emek, and Noga Harlev. On the Runtime of Chemical Reaction Networks Beyond Idealized Conditions. In 29th International Conference on DNA Computing and Molecular Programming (DNA 29). Leibniz International Proceedings in Informatics (LIPIcs), Volume 276, pp. 3:1-3:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{condon_et_al:LIPIcs.DNA.29.3, author = {Condon, Anne and Emek, Yuval and Harlev, Noga}, title = {{On the Runtime of Chemical Reaction Networks Beyond Idealized Conditions}}, booktitle = {29th International Conference on DNA Computing and Molecular Programming (DNA 29)}, pages = {3:1--3:22}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-297-6}, ISSN = {1868-8969}, year = {2023}, volume = {276}, editor = {Chen, Ho-Lin and Evans, Constantine G.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.29.3}, URN = {urn:nbn:de:0030-drops-187861}, doi = {10.4230/LIPIcs.DNA.29.3}, annote = {Keywords: chemical reaction networks, adversarial runtime, weak fairness, predicate decidability} }

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**Published in:** LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

We introduce a novel method for the rigorous quantitative evaluation of online algorithms that relaxes the "radical worst-case" perspective of classic competitive analysis. In contrast to prior work, our method, referred to as randomly infused advice (RIA), does not make any assumptions about the input sequence and does not rely on the development of designated online algorithms. Rather, it can be applied to existing online randomized algorithms, introducing a means to evaluate their performance in scenarios that lie outside the radical worst-case regime.
More concretely, an online algorithm ALG with RIA benefits from pieces of advice generated by an omniscient but not entirely reliable oracle. The crux of the new method is that the advice is provided to ALG by writing it into the buffer ℬ from which ALG normally reads its random bits, hence allowing us to augment it through a very simple and non-intrusive interface. The (un)reliability of the oracle is captured via a parameter 0 ≤ α ≤ 1 that determines the probability (per round) that the advice is successfully infused by the oracle; if the advice is not infused, which occurs with probability 1 - α, then the buffer ℬ contains fresh random bits (as in the classic online setting).
The applicability of the new RIA method is demonstrated by applying it to three extensively studied online problems: paging, uniform metrical task systems, and online set cover. For these problems, we establish new upper bounds on the competitive ratio of classic online algorithms that improve as the infusion parameter α increases. These are complemented with (often tight) lower bounds on the competitive ratio of online algorithms with RIA for the three problems.

Yuval Emek, Yuval Gil, Maciej Pacut, and Stefan Schmid. Online Algorithms with Randomly Infused Advice. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 44:1-44:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{emek_et_al:LIPIcs.ESA.2023.44, author = {Emek, Yuval and Gil, Yuval and Pacut, Maciej and Schmid, Stefan}, title = {{Online Algorithms with Randomly Infused Advice}}, booktitle = {31st Annual European Symposium on Algorithms (ESA 2023)}, pages = {44:1--44:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-295-2}, ISSN = {1868-8969}, year = {2023}, volume = {274}, editor = {G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.44}, URN = {urn:nbn:de:0030-drops-186970}, doi = {10.4230/LIPIcs.ESA.2023.44}, annote = {Keywords: Online algorithms, competitive analysis, advice} }

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**Published in:** LIPIcs, Volume 253, 26th International Conference on Principles of Distributed Systems (OPODIS 2022)

Self-stabilization is an important concept in the realm of fault-tolerant distributed computing. In this paper, we propose a new approach that relies on the properties of linear programming duality to obtain self-stabilizing approximation algorithms for distributed graph optimization problems. The power of this new approach is demonstrated by the following results:
- A self-stabilizing 2(1+ε)-approximation algorithm for minimum weight vertex cover that converges in O(logΔ /(εlog log Δ)) synchronous rounds.
- A self-stabilizing Δ-approximation algorithm for maximum weight independent set that converges in O(Δ+log^* n) synchronous rounds.
- A self-stabilizing ((2ρ+1)(1+ε))-approximation algorithm for minimum weight dominating set in ρ-arboricity graphs that converges in O((logΔ)/ε) synchronous rounds. In all of the above, Δ denotes the maximum degree. Our technique improves upon previous results in terms of time complexity while incurring only an additive O(log n) overhead to the message size. In addition, to the best of our knowledge, we provide the first self-stabilizing algorithms for the weighted versions of minimum vertex cover and maximum independent set.

Yuval Emek, Yuval Gil, and Noga Harlev. Design of Self-Stabilizing Approximation Algorithms via a Primal-Dual Approach. In 26th International Conference on Principles of Distributed Systems (OPODIS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 253, pp. 27:1-27:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{emek_et_al:LIPIcs.OPODIS.2022.27, author = {Emek, Yuval and Gil, Yuval and Harlev, Noga}, title = {{Design of Self-Stabilizing Approximation Algorithms via a Primal-Dual Approach}}, booktitle = {26th International Conference on Principles of Distributed Systems (OPODIS 2022)}, pages = {27:1--27:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-265-5}, ISSN = {1868-8969}, year = {2023}, volume = {253}, editor = {Hillel, Eshcar and Palmieri, Roberto and Rivi\`{e}re, Etienne}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2022.27}, URN = {urn:nbn:de:0030-drops-176474}, doi = {10.4230/LIPIcs.OPODIS.2022.27}, annote = {Keywords: self-stabilization, approximation algorithms, primal-dual} }

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

Constructing a shortest path between two network nodes is a fundamental task in distributed computing. This work develops schemes for the construction of shortest paths in randomized beeping networks between a predetermined source node and an arbitrary set of destination nodes. Our first scheme constructs a (single) shortest path to an arbitrary destination in O(D log log n + log³ n) rounds with high probability. Our second scheme constructs multiple shortest paths, one per each destination, in O(D log² n + log³ n) rounds with high probability.
Our schemes are based on a reduction of the above shortest path construction tasks to a decomposition of hypergraphs into bipartite hypergraphs: We develop a beeping procedure that partitions the hyperedge set of a hypergraph H = (V_H, E_H) into k = Θ (log² n) disjoint subsets F₁ ∪ ⋯ ∪ F_k = E_H such that the (sub-)hypergraph (V_H, F_i) is bipartite in the sense that there exists a vertex subset U ⊆ V such that |U ∩ e| = 1 for every e ∈ F_i. This procedure turns out to be instrumental in speeding up shortest path constructions under the beeping model.

Fabien Dufoulon, Yuval Emek, and Ran Gelles. Beeping Shortest Paths via Hypergraph Bipartite Decomposition. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 45:1-45:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{dufoulon_et_al:LIPIcs.ITCS.2023.45, author = {Dufoulon, Fabien and Emek, Yuval and Gelles, Ran}, title = {{Beeping Shortest Paths via Hypergraph Bipartite Decomposition}}, booktitle = {14th Innovations in Theoretical Computer Science Conference (ITCS 2023)}, pages = {45:1--45:24}, 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.2023.45}, URN = {urn:nbn:de:0030-drops-175485}, doi = {10.4230/LIPIcs.ITCS.2023.45}, annote = {Keywords: Beeping Networks, Shortest Paths, Hypergraph Bipartite Decomposition} }

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**Published in:** LIPIcs, Volume 246, 36th International Symposium on Distributed Computing (DISC 2022)

Introduced by Korman, Kutten, and Peleg (PODC 2005), a proof labeling scheme (PLS) is a distributed verification system dedicated to evaluating if a given configured graph satisfies a certain property. It involves a centralized prover, whose role is to provide proof that a given configured graph is a yes-instance by means of assigning labels to the nodes, and a distributed verifier, whose role is to verify the validity of the given proof via local access to the assigned labels. In this paper, we introduce the notion of a locally restricted PLS in which the prover’s power is restricted to that of a LOCAL algorithm with a polylogarithmic number of rounds. To circumvent inherent impossibilities of PLSs in the locally restricted setting, we turn to models that relax the correctness requirements by allowing the verifier to accept some no-instances as long as they are not "too far" from satisfying the property in question. To this end, we evaluate (1) distributed graph optimization problems (OptDGPs) based on the notion of an approximate proof labeling scheme (APLS) (analogous to the type of relaxation used in sequential approximation algorithms); and (2) configured graph families (CGFs) based on the notion of a testing proof labeling schemes (TPLS) (analogous to the type of relaxation used in property testing algorithms). The main contribution of the paper comes in the form of two generic compilers, one for OptDGPs and one for CGFs: given a black-box access to an APLS (resp., PLS) for a large class of OptDGPs (resp., CGFs), the compiler produces a locally restricted APLS (resp., TPLS) for the same problem, while losing at most a (1 + ε) factor in the scheme’s relaxation guarantee. An appealing feature of the two compilers is that they only require a logarithmic additive label size overhead.

Yuval Emek, Yuval Gil, and Shay Kutten. Locally Restricted Proof Labeling Schemes. In 36th International Symposium on Distributed Computing (DISC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 246, pp. 20:1-20:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{emek_et_al:LIPIcs.DISC.2022.20, author = {Emek, Yuval and Gil, Yuval and Kutten, Shay}, title = {{Locally Restricted Proof Labeling Schemes}}, booktitle = {36th International Symposium on Distributed Computing (DISC 2022)}, pages = {20:1--20:22}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-255-6}, ISSN = {1868-8969}, year = {2022}, volume = {246}, editor = {Scheideler, Christian}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2022.20}, URN = {urn:nbn:de:0030-drops-172111}, doi = {10.4230/LIPIcs.DISC.2022.20}, annote = {Keywords: proof labeling schemes, generic compilers, SLOCAL algorithms} }

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

This paper considers a variant of the online paging problem, where the online algorithm has access to multiple predictors, each producing a sequence of predictions for the page arrival times. The predictors may have occasional prediction errors and it is assumed that at least one of them makes a sublinear number of prediction errors in total. Our main result states that this assumption suffices for the design of a randomized online algorithm whose time-average regret with respect to the optimal offline algorithm tends to zero as the time tends to infinity. This holds (with different regret bounds) for both the full information access model, where in each round, the online algorithm gets the predictions of all predictors, and the bandit access model, where in each round, the online algorithm queries a single predictor.
While online algorithms that exploit inaccurate predictions have been a topic of growing interest in the last few years, to the best of our knowledge, this is the first paper that studies this topic in the context of multiple predictors for an online problem with unbounded request sequences. Moreover, to the best of our knowledge, this is also the first paper that aims for (and achieves) online algorithms with a vanishing regret for a classic online problem under reasonable assumptions.

Yuval Emek, Shay Kutten, and Yangguang Shi. Online Paging with a Vanishing Regret. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 67:1-67:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{emek_et_al:LIPIcs.ITCS.2021.67, author = {Emek, Yuval and Kutten, Shay and Shi, Yangguang}, title = {{Online Paging with a Vanishing Regret}}, booktitle = {12th Innovations in Theoretical Computer Science Conference (ITCS 2021)}, pages = {67:1--67:20}, 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.2021.67}, URN = {urn:nbn:de:0030-drops-136065}, doi = {10.4230/LIPIcs.ITCS.2021.67}, annote = {Keywords: online paging, inaccurate predictions, multiple predictors, vanishing regret, full information vs. bandit access} }

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**Published in:** LIPIcs, Volume 179, 34th International Symposium on Distributed Computing (DISC 2020)

This paper presents a randomized self-stabilizing algorithm that elects a leader r in a general n-node undirected graph and constructs a spanning tree T rooted at r. The algorithm works under the synchronous message passing network model, assuming that the nodes know a linear upper bound on n and that each edge has a unique ID known to both its endpoints (or, alternatively, assuming the KT₁ model). The highlight of this algorithm is its superior communication efficiency: It is guaranteed to send a total of Õ (n) messages, each of constant size, till stabilization, while stabilizing in Õ (n) rounds, in expectation and with high probability. After stabilization, the algorithm sends at most one constant size message per round while communicating only over the (n - 1) edges of T. In all these aspects, the communication overhead of the new algorithm is far smaller than that of the existing (mostly deterministic) self-stabilizing leader election algorithms.
The algorithm is relatively simple and relies mostly on known modules that are common in the fault free leader election literature; these modules are enhanced in various subtle ways in order to assemble them into a communication efficient self-stabilizing algorithm.

Xavier Défago, Yuval Emek, Shay Kutten, Toshimitsu Masuzawa, and Yasumasa Tamura. Communication Efficient Self-Stabilizing Leader Election. In 34th International Symposium on Distributed Computing (DISC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 179, pp. 11:1-11:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{defago_et_al:LIPIcs.DISC.2020.11, author = {D\'{e}fago, Xavier and Emek, Yuval and Kutten, Shay and Masuzawa, Toshimitsu and Tamura, Yasumasa}, title = {{Communication Efficient Self-Stabilizing Leader Election}}, booktitle = {34th International Symposium on Distributed Computing (DISC 2020)}, pages = {11:1--11:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-168-9}, ISSN = {1868-8969}, year = {2020}, volume = {179}, editor = {Attiya, Hagit}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2020.11}, URN = {urn:nbn:de:0030-drops-130892}, doi = {10.4230/LIPIcs.DISC.2020.11}, annote = {Keywords: self-stabilization, leader election, communication overhead} }

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**Published in:** LIPIcs, Volume 179, 34th International Symposium on Distributed Computing (DISC 2020)

Introduced by Korman, Kutten, and Peleg (Distributed Computing 2005), a proof labeling scheme (PLS) is a system dedicated to verifying that a given configuration graph satisfies a certain property. It is composed of a centralized prover, whose role is to generate a proof for yes-instances in the form of an assignment of labels to the nodes, and a distributed verifier, whose role is to verify the validity of the proof by local means and accept it if and only if the property is satisfied. To overcome lower bounds on the label size of PLSs for certain graph properties, Censor-Hillel, Paz, and Perry (SIROCCO 2017) introduced the notion of an approximate proof labeling scheme (APLS) that allows the verifier to accept also some no-instances as long as they are not "too far" from satisfying the property.
The goal of the current paper is to advance our understanding of the power and limitations of APLSs. To this end, we formulate the notion of APLSs in terms of distributed graph optimization problems (OptDGPs) and develop two generic methods for the design of APLSs. These methods are then applied to various classic OptDGPs, obtaining twenty-two new APLSs. An appealing characteristic of our APLSs is that they are all sequentially efficient in the sense that both the prover and the verifier are required to run in (sequential) polynomial time. On the negative side, we establish "combinatorial" lower bounds on the label size for some of the aforementioned OptDGPs that demonstrate the optimality of our corresponding APLSs. For other OptDGPs, we establish conditional lower bounds that exploit the sequential efficiency of the verifier alone (under the assumption that NP ≠ co-NP) or that of both the verifier and the prover (under the assumption that P ≠ NP, with and without the unique games conjecture).

Yuval Emek and Yuval Gil. Twenty-Two New Approximate Proof Labeling Schemes. In 34th International Symposium on Distributed Computing (DISC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 179, pp. 20:1-20:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{emek_et_al:LIPIcs.DISC.2020.20, author = {Emek, Yuval and Gil, Yuval}, title = {{Twenty-Two New Approximate Proof Labeling Schemes}}, booktitle = {34th International Symposium on Distributed Computing (DISC 2020)}, pages = {20:1--20:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-168-9}, ISSN = {1868-8969}, year = {2020}, volume = {179}, editor = {Attiya, Hagit}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2020.20}, URN = {urn:nbn:de:0030-drops-130983}, doi = {10.4230/LIPIcs.DISC.2020.20}, annote = {Keywords: proof labeling schemes, distributed graph problems, approximation algorithms} }

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**Published in:** LIPIcs, Volume 153, 23rd International Conference on Principles of Distributed Systems (OPODIS 2019)

The weighted vertex cover problem is concerned with selecting a subset of the vertices that covers a target set of edges with the objective of minimizing the total cost of the selected vertices. We consider a variant of this classic combinatorial optimization problem where the target edge set is not fully known; rather, it is characterized by a probability distribution. Adhering to the model of two-stage stochastic optimization, the execution is divided into two stages so that in the first stage, the decision maker selects some of the vertices based on the probabilistic forecast of the target edge set. Then, in the second stage, the edges in the target set are revealed and in order to cover them, the decision maker can augment the vertex subset selected in the first stage with additional vertices. However, in the second stage, the vertex cost increases by some inflation factor, so the second stage selection becomes more expensive.
The current paper studies the two-stage stochastic vertex cover problem in the realm of distributed graph algorithms, where the decision making process (in both stages) is distributed among the vertices of the graph. By combining the stochastic optimization toolbox with recent advances in distributed algorithms for weighted vertex cover, we develop an algorithm that runs in time O(log (Δ) / ε), sends O(m) messages in total, and guarantees to approximate the optimal solution within a (3 + ε)-ratio, where m is the number of edges in the graph, Δ is its maximum degree, and 0 < ε < 1 is a performance parameter.

Yuval Emek, Noga Harlev, and Taisuke Izumi. Towards Distributed Two-Stage Stochastic Optimization. In 23rd International Conference on Principles of Distributed Systems (OPODIS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 153, pp. 32:1-32:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{emek_et_al:LIPIcs.OPODIS.2019.32, author = {Emek, Yuval and Harlev, Noga and Izumi, Taisuke}, title = {{Towards Distributed Two-Stage Stochastic Optimization}}, booktitle = {23rd International Conference on Principles of Distributed Systems (OPODIS 2019)}, pages = {32:1--32:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-133-7}, ISSN = {1868-8969}, year = {2020}, volume = {153}, editor = {Felber, Pascal and Friedman, Roy and Gilbert, Seth and Miller, Avery}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2019.32}, URN = {urn:nbn:de:0030-drops-118187}, doi = {10.4230/LIPIcs.OPODIS.2019.32}, annote = {Keywords: weighted vertex cover, distributed graph algorithms, two-stage stochastic optimization, primal-dual} }

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

In many models for large-scale computation, decomposition of the problem is key to efficient algorithms. For distance-related graph problems, it is often crucial that such a decomposition results in clusters of small diameter, while the probability that an edge is cut by the decomposition scales linearly with the length of the edge. There is a large body of literature on low diameter graph decomposition with small edge cutting probabilities, with all existing techniques heavily building on single source shortest paths (SSSP) computations. Unfortunately, in many theoretical models for large-scale computations, the SSSP task constitutes a complexity bottleneck. Therefore, it is desirable to replace exact SSSP computations with approximate ones. However this imposes a fundamental challenge since the existing constructions of low diameter graph decomposition with small edge cutting probabilities inherently rely on the subtractive form of the triangle inequality, which fails to hold under distance approximation.
The current paper overcomes this obstacle by developing a technique termed blurry ball growing. By combining this technique with a clever algorithmic idea of Miller et al. (SPAA 2013), we obtain a construction of low diameter decompositions with small edge cutting probabilities which replaces exact SSSP computations by (a small number of) approximate ones. The utility of our approach is showcased by deriving efficient algorithms that work in the CONGEST, PRAM, and semi-streaming models of computation. As an application, we obtain metric tree embedding algorithms in the vein of Bartal (FOCS 1996) whose computational complexities in these models are optimal up to polylogarithmic factors. Our embeddings have the additional useful property that the tree can be mapped back to the original graph such that each edge is "used" only logaritmically many times, which is of interest for capacitated problems and simulating CONGEST algorithms on the tree into which the graph is embedded.

Ruben Becker, Yuval Emek, and Christoph Lenzen. Low Diameter Graph Decompositions by Approximate Distance Computation. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 50:1-50:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{becker_et_al:LIPIcs.ITCS.2020.50, author = {Becker, Ruben and Emek, Yuval and Lenzen, Christoph}, title = {{Low Diameter Graph Decompositions by Approximate Distance Computation}}, booktitle = {11th Innovations in Theoretical Computer Science Conference (ITCS 2020)}, pages = {50:1--50:29}, 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.2020.50}, URN = {urn:nbn:de:0030-drops-117355}, doi = {10.4230/LIPIcs.ITCS.2020.50}, annote = {Keywords: graph decompositions, metric tree embeddings, distributed graph algorithms, parallel graph algorithms, (semi-)streaming graph algorithms} }

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**Published in:** LIPIcs, Volume 146, 33rd International Symposium on Distributed Computing (DISC 2019)

Given an undirected graph with integer edge lengths, we study the problem of approximating the distances in the graph by a spanning tree based on the notion of stretch. Our main contribution is a distributed algorithm in the CONGEST model of computation that constructs a random spanning tree with the guarantee that the expected stretch of every edge is O(log^{3} n), where n is the number of nodes in the graph. If the graph is unweighted, then this algorithm can be implemented to run in O(D) rounds, where D is the hop-diameter of the graph, thus being asymptotically optimal. In the weighted case, the run-time of our algorithm matches the currently best known bound for exact distance computations, i.e., O~ (min{sqrt{n D}, sqrt{n} D^{1 / 4} + n^{3 / 5} + D}). We stress that this is the first distributed construction of spanning trees leading to poly-logarithmic expected stretch with non-trivial running time.

Ruben Becker, Yuval Emek, Mohsen Ghaffari, and Christoph Lenzen. Distributed Algorithms for Low Stretch Spanning Trees. In 33rd International Symposium on Distributed Computing (DISC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 146, pp. 4:1-4:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{becker_et_al:LIPIcs.DISC.2019.4, author = {Becker, Ruben and Emek, Yuval and Ghaffari, Mohsen and Lenzen, Christoph}, title = {{Distributed Algorithms for Low Stretch Spanning Trees}}, booktitle = {33rd International Symposium on Distributed Computing (DISC 2019)}, pages = {4:1--4:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-126-9}, ISSN = {1868-8969}, year = {2019}, volume = {146}, editor = {Suomela, Jukka}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2019.4}, URN = {urn:nbn:de:0030-drops-113116}, doi = {10.4230/LIPIcs.DISC.2019.4}, annote = {Keywords: distributed graph algorithms, low-stretch spanning trees, CONGEST model, ball decomposition, star decomposition} }

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**Published in:** LIPIcs, Volume 146, 33rd International Symposium on Distributed Computing (DISC 2019)

A new spanner construction algorithm is presented, working under the LOCAL model with unique edge IDs. Given an n-node communication graph, a spanner with a constant stretch and O(n^{1 + epsilon}) edges (for an arbitrarily small constant epsilon > 0) is constructed in a constant number of rounds sending O(n^{1 + epsilon}) messages whp. Consequently, we conclude that every t-round LOCAL algorithm can be transformed into an O(t)-round LOCAL algorithm that sends O(t * n^{1 + epsilon}) messages whp. This improves upon all previous message-reduction schemes for LOCAL algorithms that incur a log^{Omega (1)} n blow-up of the round complexity.

Shimon Bitton, Yuval Emek, Taisuke Izumi, and Shay Kutten. Message Reduction in the LOCAL Model Is a Free Lunch. In 33rd International Symposium on Distributed Computing (DISC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 146, pp. 7:1-7:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{bitton_et_al:LIPIcs.DISC.2019.7, author = {Bitton, Shimon and Emek, Yuval and Izumi, Taisuke and Kutten, Shay}, title = {{Message Reduction in the LOCAL Model Is a Free Lunch}}, booktitle = {33rd International Symposium on Distributed Computing (DISC 2019)}, pages = {7:1--7:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-126-9}, ISSN = {1868-8969}, year = {2019}, volume = {146}, editor = {Suomela, Jukka}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2019.7}, URN = {urn:nbn:de:0030-drops-113145}, doi = {10.4230/LIPIcs.DISC.2019.7}, annote = {Keywords: distributed graph algorithms, spanner, LOCAL model, message complexity} }

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**Published in:** LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019)

The disjoint set cover (DSC) problem is a fundamental combinatorial optimization problem concerned with partitioning the (hyper)edges of a hypergraph into (pairwise disjoint) clusters so that the number of clusters that cover all nodes is maximized. In its online version, the edges arrive one-by-one and should be assigned to clusters in an irrevocable fashion without knowing the future edges. This paper investigates the competitiveness of online DSC algorithms. Specifically, we develop the first (randomized) online DSC algorithm that guarantees a poly-logarithmic (O(log^{2} n)) competitive ratio without prior knowledge of the hypergraph’s minimum degree. On the negative side, we prove that the competitive ratio of any randomized online DSC algorithm must be at least Omega((log n)/(log log n)) (even if the online algorithm does know the minimum degree in advance), thus establishing the first lower bound on the competitive ratio of randomized online DSC algorithms.

Yuval Emek, Adam Goldbraikh, and Erez Kantor. Online Disjoint Set Cover Without Prior Knowledge. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 44:1-44:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{emek_et_al:LIPIcs.ESA.2019.44, author = {Emek, Yuval and Goldbraikh, Adam and Kantor, Erez}, title = {{Online Disjoint Set Cover Without Prior Knowledge}}, booktitle = {27th Annual European Symposium on Algorithms (ESA 2019)}, pages = {44:1--44:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-124-5}, ISSN = {1868-8969}, year = {2019}, volume = {144}, editor = {Bender, Michael A. and Svensson, Ola and Herman, Grzegorz}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2019.44}, URN = {urn:nbn:de:0030-drops-111654}, doi = {10.4230/LIPIcs.ESA.2019.44}, annote = {Keywords: disjoint set cover, online algorithms, competitive analysis, competitiveness with high probability} }

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**Published in:** LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019)

We study network coordination problems, as captured by the setting of generalized network design (Emek et al., STOC 2018), in the face of uncertainty resulting from partial information that the network users hold regarding the actions of their peers. This uncertainty is formalized using Alon et al.’s Bayesian ignorance framework (TCS 2012). While the approach of Alon et al. is purely combinatorial, the current paper takes into account computational considerations: Our main technical contribution is the development of (strongly) polynomial time algorithms for local decision making in the face of Bayesian uncertainty.

Yuval Emek, Shay Kutten, Ron Lavi, and Yangguang Shi. Bayesian Generalized Network Design. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 45:1-45:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{emek_et_al:LIPIcs.ESA.2019.45, author = {Emek, Yuval and Kutten, Shay and Lavi, Ron and Shi, Yangguang}, title = {{Bayesian Generalized Network Design}}, booktitle = {27th Annual European Symposium on Algorithms (ESA 2019)}, pages = {45:1--45:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-124-5}, ISSN = {1868-8969}, year = {2019}, volume = {144}, editor = {Bender, Michael A. and Svensson, Ola and Herman, Grzegorz}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2019.45}, URN = {urn:nbn:de:0030-drops-111660}, doi = {10.4230/LIPIcs.ESA.2019.45}, annote = {Keywords: approximation algorithms, Bayesian competitive ratio, Bayesian ignorance, generalized network design, diseconomies of scale, energy consumption, smoothness, best response dynamics} }

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Track C: Foundations of Networks and Multi-Agent Systems: Models, Algorithms and Information Management

**Published in:** LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

Addressing a fundamental problem in programmable matter, we present the first deterministic algorithm to elect a unique leader in a system of connected amoebots assuming only that amoebots are initially contracted. Previous algorithms either used randomization, made various assumptions (shapes with no holes, or known shared chirality), or elected several co-leaders in some cases.
Some of the building blocks we introduce in constructing the algorithm are of interest by themselves, especially the procedure we present for reaching common chirality among the amoebots. Given the leader election and the chirality agreement building block, it is known that various tasks in programmable matter can be performed or improved.
The main idea of the new algorithm is the usage of the ability of the amoebots to move, which previous leader election algorithms have not used.

Yuval Emek, Shay Kutten, Ron Lavi, and William K. Moses Jr.. Deterministic Leader Election in Programmable Matter. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 140:1-140:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{emek_et_al:LIPIcs.ICALP.2019.140, author = {Emek, Yuval and Kutten, Shay and Lavi, Ron and Moses Jr., William K.}, title = {{Deterministic Leader Election in Programmable Matter}}, booktitle = {46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)}, pages = {140:1--140:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-109-2}, ISSN = {1868-8969}, year = {2019}, volume = {132}, editor = {Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.140}, URN = {urn:nbn:de:0030-drops-107169}, doi = {10.4230/LIPIcs.ICALP.2019.140}, annote = {Keywords: programmable matter, geometric amoebot model, leader election} }

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**Published in:** LIPIcs, Volume 125, 22nd International Conference on Principles of Distributed Systems (OPODIS 2018)

What can be computed by a network of n randomized finite state machines communicating under the stone age model (Emek & Wattenhofer, PODC 2013)? The inherent linear upper bound on the total space of the network implies that its global computational power is not larger than that of a randomized linear space Turing machine, but is this tight? We answer this question affirmatively for bounded degree networks by introducing a stone age algorithm (operating under the most restrictive form of the model) that given a designated I/O node, constructs a tour in the network that enables the simulation of the Turing machine's tape. To construct the tour with high probability, we first show how to 2-hop color the network concurrently with building a spanning tree.

Yehuda Afek, Yuval Emek, and Noa Kolikant. The Synergy of Finite State Machines. In 22nd International Conference on Principles of Distributed Systems (OPODIS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 125, pp. 22:1-22:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{afek_et_al:LIPIcs.OPODIS.2018.22, author = {Afek, Yehuda and Emek, Yuval and Kolikant, Noa}, title = {{The Synergy of Finite State Machines}}, booktitle = {22nd International Conference on Principles of Distributed Systems (OPODIS 2018)}, pages = {22:1--22:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-098-9}, ISSN = {1868-8969}, year = {2019}, volume = {125}, editor = {Cao, Jiannong and Ellen, Faith and Rodrigues, Luis and Ferreira, Bernardo}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2018.22}, URN = {urn:nbn:de:0030-drops-100825}, doi = {10.4230/LIPIcs.OPODIS.2018.22}, annote = {Keywords: finite state machines, stone-age model, beeping communication scheme, distributed network computability} }

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**Published in:** LIPIcs, Volume 121, 32nd International Symposium on Distributed Computing (DISC 2018)

This paper studies a variant of the leader election problem under the stone age model (Emek and Wattenhofer, PODC 2013) that considers a network of n randomized finite automata with very weak communication capabilities (a multi-frequency asynchronous generalization of the beeping model's communication scheme). Since solving the classic leader election problem is impossible even in more powerful models, we consider a relaxed variant, referred to as k-leader selection, in which a leader should be selected out of at most k initial candidates. Our main contribution is an algorithm that solves k-leader selection for bounded k in the aforementioned stone age model. On (general topology) graphs of diameter D, this algorithm runs in O~(D) time and succeeds with high probability. The assumption that k is bounded turns out to be unavoidable: we prove that if k = omega (1), then no algorithm in this model can solve k-leader selection with a (positive) constant probability.

Yehuda Afek, Yuval Emek, and Noa Kolikant. Selecting a Leader in a Network of Finite State Machines. In 32nd International Symposium on Distributed Computing (DISC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 121, pp. 4:1-4:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{afek_et_al:LIPIcs.DISC.2018.4, author = {Afek, Yehuda and Emek, Yuval and Kolikant, Noa}, title = {{Selecting a Leader in a Network of Finite State Machines}}, booktitle = {32nd International Symposium on Distributed Computing (DISC 2018)}, pages = {4:1--4:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-092-7}, ISSN = {1868-8969}, year = {2018}, volume = {121}, editor = {Schmid, Ulrich and Widder, Josef}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2018.4}, URN = {urn:nbn:de:0030-drops-97933}, doi = {10.4230/LIPIcs.DISC.2018.4}, annote = {Keywords: stone age model, beeping communication scheme, leader election, k-leader selection, randomized finite state machines, asynchronous scheduler} }

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Brief Announcement

**Published in:** LIPIcs, Volume 91, 31st International Symposium on Distributed Computing (DISC 2017)

What can be computed by a network of n randomized finite state machines communicating under the stone age model (a generalization of the beeping model’s communication scheme)? The inherent linear upper bound on the total space of the network implies that its global computational power is not larger than that of a randomized linear space Turing machine, but is this tight? The reported reseach answers this question affirmatively for bounded degree networks by introducing a stone age algorithm (operating under the most restrictive form of the model) that given a designated I/O node, constructs a tour in the network that enables the simulation of the Turing machine’s tape. To construct the tour, it is first shown how to 2-hop color the network concurrently with building a spanning tree with high probability.

Yehuda Afek, Yuval Emek, and Noa Kolikant. Brief Announcement: The Synergy of Finite State Machines. In 31st International Symposium on Distributed Computing (DISC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 91, pp. 42:1-42:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{afek_et_al:LIPIcs.DISC.2017.42, author = {Afek, Yehuda and Emek, Yuval and Kolikant, Noa}, title = {{Brief Announcement: The Synergy of Finite State Machines}}, booktitle = {31st International Symposium on Distributed Computing (DISC 2017)}, pages = {42:1--42:3}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-053-8}, ISSN = {1868-8969}, year = {2017}, volume = {91}, editor = {Richa, Andr\'{e}a}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2017.42}, URN = {urn:nbn:de:0030-drops-80072}, doi = {10.4230/LIPIcs.DISC.2017.42}, annote = {Keywords: beeping communication, finite state machine, stone age model, distributed network complexity} }

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**Published in:** LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)

For the game of Cops and Robbers, it is known that in 1-cop-win graphs, the cop can capture the robber in O(n) time, and that there exist graphs in which this capture time is tight. When k >= 2, a simple counting argument shows that in k-cop-win graphs, the capture time is at most O(n^{k + 1}), however, no non-trivial lower bounds were previously known; indeed, in their 2011 book, Bonato and Nowakowski ask whether this upper bound can be improved. In this paper, the question of Bonato and Nowakowski is answered on the negative, proving that the O(n^{k + 1}) bound is asymptotically tight for any constant k >= 2. This yields a surprising gap in the capture time complexities between the 1-cop and the 2-cop cases.

Sebastian Brandt, Yuval Emek, Jara Uitto, and Roger Wattenhofer. A Tight Lower Bound for the Capture Time of the Cops and Robbers Game. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 82:1-82:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{brandt_et_al:LIPIcs.ICALP.2017.82, author = {Brandt, Sebastian and Emek, Yuval and Uitto, Jara and Wattenhofer, Roger}, title = {{A Tight Lower Bound for the Capture Time of the Cops and Robbers Game}}, booktitle = {44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)}, pages = {82:1--82:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-041-5}, ISSN = {1868-8969}, year = {2017}, volume = {80}, editor = {Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.82}, URN = {urn:nbn:de:0030-drops-74134}, doi = {10.4230/LIPIcs.ICALP.2017.82}, annote = {Keywords: cops and robbers, capture time, lower bound} }