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Track A: Algorithms, Complexity and Games

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

We study sublinear time algorithms for the traveling salesman problem (TSP). First, we focus on the closely related maximum path cover problem, which asks for a collection of vertex disjoint paths that include the maximum number of edges. We show that for any fixed ε > 0, there is an algorithm that (1/2 - ε)-approximates the maximum path cover size of an n-vertex graph in Õ(n) time. This improves upon a (3/8-ε)-approximate Õ(n √n)-time algorithm of Chen, Kannan, and Khanna [ICALP'20].
Equipped with our path cover algorithm, we give an Õ(n) time algorithm that estimates the cost of (1,2)-TSP within a factor of (1.5+ε) which is an improvement over a folklore (1.75 + ε)-approximate Õ(n)-time algorithm, as well as a (1.625+ε)-approximate Õ(n√n)-time algorithm of [CHK ICALP'20]. For graphic TSP, we present an Õ(n) algorithm that estimates the cost of graphic TSP within a factor of 1.83 which is an improvement over a 1.92-approximate Õ(n) time algorithm due to [CHK ICALP'20, Behnezhad FOCS'21]. We show that the approximation can be further improved to 1.66 using n^{2-Ω(1)} time.
All of our Õ(n) time algorithms are information-theoretically time-optimal up to polylog n factors. Additionally, we show that our approximation guarantees for path cover and (1,2)-TSP hit a natural barrier: We show better approximations require better sublinear time algorithms for the well-studied maximum matching problem.

Soheil Behnezhad, Mohammad Roghani, Aviad Rubinstein, and Amin Saberi. Sublinear Algorithms for TSP via Path Covers. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 19:1-19:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{behnezhad_et_al:LIPIcs.ICALP.2024.19, author = {Behnezhad, Soheil and Roghani, Mohammad and Rubinstein, Aviad and Saberi, Amin}, title = {{Sublinear Algorithms for TSP via Path Covers}}, booktitle = {51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)}, pages = {19:1--19:16}, 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.2024.19}, URN = {urn:nbn:de:0030-drops-201623}, doi = {10.4230/LIPIcs.ICALP.2024.19}, annote = {Keywords: Sublinear Algorithms, Traveling Salesman Problem, Approximation Algorithm, (1, 2)-TSP, Graphic TSP} }

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

Motivated by large-market applications such as crowdsourcing, we revisit the problem of budget-feasible mechanism design under a "small-bidder assumption". Anari, Goel, and Nikzad (2018) gave a mechanism that has optimal competitive ratio 1-1/e on worst-case instances. However, we observe that on many realistic instances, their mechanism is significantly outperformed by a simpler open clock auction by Ensthaler and Giebe (2014), although the open clock auction only achieves competitive ratio 1/2 in the worst case. Is there a mechanism that gets the best of both worlds, i.e., a mechanism that is worst-case optimal and performs favorably on realistic instances? To answer this question, we initiate the study of beyond worst-case budget-feasible mechanism design.
Our first main result is the design and the analysis of a natural mechanism that gives an affirmative answer to our question above:
- We prove that on every instance, our mechanism performs at least as good as all uniform mechanisms, including Anari, Goel, and Nikzad’s and Ensthaler and Giebe’s mechanisms.
- Moreover, we empirically evaluate our mechanism on various realistic instances and observe that it beats the worst-case 1-1/e competitive ratio by a large margin and compares favorably to both mechanisms mentioned above.
Our second main result is more interesting in theory: We show that in the semi-adversarial model of budget-smoothed analysis, where the adversary designs a single worst-case market for a distribution of budgets, our mechanism is optimal among all (including non-uniform) mechanisms; furthermore our mechanism guarantees a strictly better-than-(1-1/e) expected competitive ratio for any non-trivial budget distribution regardless of the market. (In contrast, given any bounded range of budgets, we can construct a single market where Anari, Goel, and Nikzad’s mechanism achieves only 1-1/e competitive ratio for every budget in this range.) We complement the positive result with a characterization of the worst-case markets for any given budget distribution and prove a fairly robust hardness result that holds against any budget distribution and any mechanism.

Aviad Rubinstein and Junyao Zhao. Beyond Worst-Case Budget-Feasible Mechanism Design. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 93:1-93:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{rubinstein_et_al:LIPIcs.ITCS.2023.93, author = {Rubinstein, Aviad and Zhao, Junyao}, title = {{Beyond Worst-Case Budget-Feasible Mechanism Design}}, booktitle = {14th Innovations in Theoretical Computer Science Conference (ITCS 2023)}, pages = {93:1--93:22}, 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.2023.93}, URN = {urn:nbn:de:0030-drops-175969}, doi = {10.4230/LIPIcs.ITCS.2023.93}, annote = {Keywords: Procurement auctions, Mechanism design, Beyond worst-case analysis} }

Document

Track A: Algorithms, Complexity and Games

**Published in:** LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

In this work we give two new algorithms that use similar techniques for (non-monotone) submodular function maximization subject to a cardinality constraint. The first is an offline fixed-parameter tractable algorithm that guarantees a 0.539-approximation for all non-negative submodular functions. The second algorithm works in the random-order streaming model. It guarantees a (1/2+c)-approximation for symmetric functions, and we complement it by showing that no space-efficient algorithm can beat 1/2 for asymmetric functions. To the best of our knowledge this is the first provable separation between symmetric and asymmetric submodular function maximization.

Aviad Rubinstein and Junyao Zhao. Maximizing Non-Monotone Submodular Functions over Small Subsets: Beyond 1/2-Approximation. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 106:1-106:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{rubinstein_et_al:LIPIcs.ICALP.2022.106, author = {Rubinstein, Aviad and Zhao, Junyao}, title = {{Maximizing Non-Monotone Submodular Functions over Small Subsets: Beyond 1/2-Approximation}}, booktitle = {49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)}, pages = {106:1--106:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-235-8}, ISSN = {1868-8969}, year = {2022}, volume = {229}, editor = {Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.106}, URN = {urn:nbn:de:0030-drops-164478}, doi = {10.4230/LIPIcs.ICALP.2022.106}, annote = {Keywords: Submodular optimization, Fixed-parameter tractability, Random-order streaming} }

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

The greedy algorithm for monotone submodular function maximization subject to cardinality constraint is guaranteed to approximate the optimal solution to within a 1-1/e factor. Although it is well known that this guarantee is essentially tight in the worst case - for greedy and in fact any efficient algorithm, experiments show that greedy performs better in practice. We observe that for many applications in practice, the empirical distribution of the budgets (i.e., cardinality constraints) is supported on a wide range, and moreover, all the existing hardness results in theory break under a large perturbation of the budget.
To understand the effect of the budget from both algorithmic and hardness perspectives, we introduce a new notion of budget-smoothed analysis. We prove that greedy is optimal for every budget distribution, and we give a characterization for the worst-case submodular functions. Based on these results, we show that on the algorithmic side, under realistic budget distributions, greedy and related algorithms enjoy provably better approximation guarantees, that hold even for worst-case functions, and on the hardness side, there exist hard functions that are fairly robust to all the budget distributions.

Aviad Rubinstein and Junyao Zhao. Budget-Smoothed Analysis for Submodular Maximization. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 113:1-113:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{rubinstein_et_al:LIPIcs.ITCS.2022.113, author = {Rubinstein, Aviad and Zhao, Junyao}, title = {{Budget-Smoothed Analysis for Submodular Maximization}}, booktitle = {13th Innovations in Theoretical Computer Science Conference (ITCS 2022)}, pages = {113:1--113:23}, 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.2022.113}, URN = {urn:nbn:de:0030-drops-157095}, doi = {10.4230/LIPIcs.ITCS.2022.113}, annote = {Keywords: Submodular optimization, Beyond worst-case analysis, Greedy algorithms, Hardness of approximation} }

Document

Track A: Algorithms, Complexity and Games

**Published in:** LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)

The edit distance (ED) and longest common subsequence (LCS) are two fundamental problems which quantify how similar two strings are to one another. In this paper, we first consider these problems in the asymmetric streaming model introduced by Andoni, Krauthgamer and Onak [Andoni et al., 2010] (FOCS'10) and Saks and Seshadhri [Saks and Seshadhri, 2013] (SODA'13). In this model we have random access to one string and streaming access the other one. Our main contribution is a constant factor approximation algorithm for ED with memory Õ(n^δ) for any constant δ > 0. In addition to this, we present an upper bound of Õ _ε(√n) on the memory needed to approximate ED or LCS within a factor 1±ε. All our algorithms are deterministic and run in polynomial time in a single pass.
We further study small-space approximation algorithms for ED, LCS, and longest increasing sequence (LIS) in the non-streaming setting. Here, we design algorithms that achieve 1 ± ε approximation for all three problems, where ε > 0 can be any constant and even slightly sub-constant. Our algorithms only use poly-logarithmic space while maintaining a polynomial running time. This significantly improves previous results in terms of space complexity, where all known results need to use space at least Ω(√n). Our algorithms make novel use of triangle inequality and carefully designed recursions to save space, which can be of independent interest.

Kuan Cheng, Alireza Farhadi, MohammadTaghi Hajiaghayi, Zhengzhong Jin, Xin Li, Aviad Rubinstein, Saeed Seddighin, and Yu Zheng. Streaming and Small Space Approximation Algorithms for Edit Distance and Longest Common Subsequence. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 54:1-54:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{cheng_et_al:LIPIcs.ICALP.2021.54, author = {Cheng, Kuan and Farhadi, Alireza and Hajiaghayi, MohammadTaghi and Jin, Zhengzhong and Li, Xin and Rubinstein, Aviad and Seddighin, Saeed and Zheng, Yu}, title = {{Streaming and Small Space Approximation Algorithms for Edit Distance and Longest Common Subsequence}}, booktitle = {48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)}, pages = {54:1--54:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-195-5}, ISSN = {1868-8969}, year = {2021}, volume = {198}, editor = {Bansal, Nikhil and Merelli, Emanuela and Worrell, James}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.54}, URN = {urn:nbn:de:0030-drops-141236}, doi = {10.4230/LIPIcs.ICALP.2021.54}, annote = {Keywords: Edit Distance, Longest Common Subsequence, Longest Increasing Subsequence, Space Efficient Algorithm, Approximation Algorithm} }

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

We formulate a new hardness assumption, the Strongish Planted Clique Hypothesis (SPCH), which postulates that any algorithm for planted clique must run in time n^Ω(log n) (so that the state-of-the-art running time of n^O(log n) is optimal up to a constant in the exponent).
We provide two sets of applications of the new hypothesis. First, we show that SPCH implies (nearly) tight inapproximability results for the following well-studied problems in terms of the parameter k: Densest k-Subgraph, Smallest k-Edge Subgraph, Densest k-Subhypergraph, Steiner k-Forest, and Directed Steiner Network with k terminal pairs. For example, we show, under SPCH, that no polynomial time algorithm achieves o(k)-approximation for Densest k-Subgraph. This inapproximability ratio improves upon the previous best k^o(1) factor from (Chalermsook et al., FOCS 2017). Furthermore, our lower bounds hold even against fixed-parameter tractable algorithms with parameter k.
Our second application focuses on the complexity of graph pattern detection. For both induced and non-induced graph pattern detection, we prove hardness results under SPCH, improving the running time lower bounds obtained by (Dalirrooyfard et al., STOC 2019) under the Exponential Time Hypothesis.

Pasin Manurangsi, Aviad Rubinstein, and Tselil Schramm. The Strongish Planted Clique Hypothesis and Its Consequences. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 10:1-10:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{manurangsi_et_al:LIPIcs.ITCS.2021.10, author = {Manurangsi, Pasin and Rubinstein, Aviad and Schramm, Tselil}, title = {{The Strongish Planted Clique Hypothesis and Its Consequences}}, booktitle = {12th Innovations in Theoretical Computer Science Conference (ITCS 2021)}, pages = {10:1--10:21}, 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.2021.10}, URN = {urn:nbn:de:0030-drops-135491}, doi = {10.4230/LIPIcs.ITCS.2021.10}, annote = {Keywords: Planted Clique, Densest k-Subgraph, Hardness of Approximation} }

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

The use of monotonicity and Tarski’s theorem in existence proofs of equilibria is very widespread in economics, while Tarski’s theorem is also often used for similar purposes in the context of verification. However, there has been relatively little in the way of analysis of the complexity of finding the fixed points and equilibria guaranteed by this result. We study a computational formalism based on monotone functions on the d-dimensional grid with sides of length N, and their fixed points, as well as the closely connected subject of supermodular games and their equilibria. It is known that finding some (any) fixed point of a monotone function can be done in time log^d N, and we show it requires at least log^2 N function evaluations already on the 2-dimensional grid, even for randomized algorithms. We show that the general Tarski problem of finding some fixed point, when the monotone function is given succinctly (by a boolean circuit), is in the class PLS of problems solvable by local search and, rather surprisingly, also in the class PPAD. Finding the greatest or least fixed point guaranteed by Tarski’s theorem, however, requires d ⋅ N steps, and is NP-hard in the white box model. For supermodular games, we show that finding an equilibrium in such games is essentially computationally equivalent to the Tarski problem, and finding the maximum or minimum equilibrium is similarly harder. Interestingly, two-player supermodular games where the strategy space of one player is one-dimensional can be solved in O(log N) steps. We also show that computing (approximating) the value of Condon’s (Shapley’s) stochastic games reduces to the Tarski problem. An important open problem highlighted by this work is proving a Ω(log^d N) lower bound for small fixed dimension d ≥ 3.

Kousha Etessami, Christos Papadimitriou, Aviad Rubinstein, and Mihalis Yannakakis. Tarski’s Theorem, Supermodular Games, and the Complexity of Equilibria. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 18:1-18:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{etessami_et_al:LIPIcs.ITCS.2020.18, author = {Etessami, Kousha and Papadimitriou, Christos and Rubinstein, Aviad and Yannakakis, Mihalis}, title = {{Tarski’s Theorem, Supermodular Games, and the Complexity of Equilibria}}, booktitle = {11th Innovations in Theoretical Computer Science Conference (ITCS 2020)}, pages = {18:1--18:19}, 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.2020.18}, URN = {urn:nbn:de:0030-drops-117037}, doi = {10.4230/LIPIcs.ITCS.2020.18}, annote = {Keywords: Tarski’s theorem, supermodular games, monotone functions, lattices, fixed points, Nash equilibria, computational complexity, PLS, PPAD, stochastic games, oracle model, lower bounds} }

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

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].

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} }

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

The Longest Common Subsequence (LCS) is one of the most basic similarity measures and it captures important applications in bioinformatics and text analysis. Following the SETH-based nearly-quadratic time lower bounds for LCS from recent years, it is a major open problem to understand the complexity of approximate LCS.
In the last ITCS [AB17] drew an interesting connection between this problem and the area of circuit complexity:
they proved that approximation algorithms for LCS in deterministic truly-subquadratic time imply new circuit lower bounds (E^NP does not have non-uniform linear-size Valiant Series Parallel circuits).
In this work, we strengthen this connection between approximate LCS and circuit complexity by applying the Distributed PCP framework of [ARW17].
We obtain a reduction that holds against much larger approximation factors (super-constant versus 1+o(1)), yields a lower bound for a larger class of circuits (linear-size NC^1), and is also easier to analyze.

Amir Abboud and Aviad Rubinstein. Fast and Deterministic Constant Factor Approximation Algorithms for LCS Imply New Circuit Lower Bounds. In 9th Innovations in Theoretical Computer Science Conference (ITCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 94, pp. 35:1-35:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{abboud_et_al:LIPIcs.ITCS.2018.35, author = {Abboud, Amir and Rubinstein, Aviad}, title = {{Fast and Deterministic Constant Factor Approximation Algorithms for LCS Imply New Circuit Lower Bounds}}, booktitle = {9th Innovations in Theoretical Computer Science Conference (ITCS 2018)}, pages = {35:1--35:14}, 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.2018.35}, URN = {urn:nbn:de:0030-drops-83490}, doi = {10.4230/LIPIcs.ITCS.2018.35}, annote = {Keywords: Distributed PCP, Longest Common Subsequence, Fine-grained Complexity, Strong Exponential Time Hypothesis} }

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

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).

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} }

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

We consider the algorithmic problem of community detection in networks. Given an undirected friendship graph G, a subset
S of vertices is an (a,b)-community if: * Every member of the community is friends with an (a)-fraction of the community; and
* every non-member is friends with at most a (b)-fraction of the
community.
[Arora, Ge, Sachdeva, Schoenebeck 2012] gave a quasi-polynomial
time algorithm for enumerating all the (a,b)-communities
for any constants a>b.
Here, we prove that, assuming the Exponential Time Hypothesis (ETH),
quasi-polynomial time is in fact necessary - and even for a much weaker
approximation desideratum. Namely, distinguishing between:
* G contains an (1,o(1))-community; and
* G does not contain a (b,b+o(1))-community
for any b.
We also prove that counting the number of (1,o(1))-communities
requires quasi-polynomial time assuming the weaker #ETH.

Aviad Rubinstein. Detecting communities is Hard (And Counting Them is Even Harder). In 8th Innovations in Theoretical Computer Science Conference (ITCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 67, pp. 42:1-42:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{rubinstein:LIPIcs.ITCS.2017.42, author = {Rubinstein, Aviad}, title = {{Detecting communities is Hard (And Counting Them is Even Harder)}}, booktitle = {8th Innovations in Theoretical Computer Science Conference (ITCS 2017)}, pages = {42:1--42:13}, 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.2017.42}, URN = {urn:nbn:de:0030-drops-81496}, doi = {10.4230/LIPIcs.ITCS.2017.42}, annote = {Keywords: Community detection, stable communities, quasipolynomial time} }

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

We prove that, assuming the exponential time hypothesis, finding an epsilon-approximately optimal symmetric signaling scheme in a two-player zero-sum game requires quasi-polynomial time. This is tight by [Cheng et al., FOCS'15] and resolves an open question of [Dughmi, FOCS'14]. We also prove that finding a multiplicative approximation is NP-hard.
We also introduce a new model where a dishonest signaler may publicly commit to use one scheme, but post signals according to a different scheme. For this model, we prove that even finding a (1-2^{-n})-approximately optimal scheme is NP-hard.

Aviad Rubinstein. Honest Signaling in Zero-Sum Games Is Hard, and Lying Is Even Harder. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 77:1-77:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{rubinstein:LIPIcs.ICALP.2017.77, author = {Rubinstein, Aviad}, title = {{Honest Signaling in Zero-Sum Games Is Hard, and Lying Is Even Harder}}, booktitle = {44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)}, pages = {77:1--77:13}, 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.2017.77}, URN = {urn:nbn:de:0030-drops-74057}, doi = {10.4230/LIPIcs.ICALP.2017.77}, annote = {Keywords: Signaling, Zero-sum Games, Algorithmic Game Theory, birthday repetition} }

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