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Documents authored by Melissourgos, Themistoklis

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.72
On the Smoothed Complexity of Combinatorial Local Search

Authors: Yiannis Giannakopoulos, Alexander Grosz, and Themistoklis Melissourgos

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

Abstract
We propose a unifying framework for smoothed analysis of combinatorial local optimization problems, and show how a diverse selection of problems within the complexity class PLS can be cast within this model. This abstraction allows us to identify key structural properties, and corresponding parameters, that determine the smoothed running time of local search dynamics. We formalize this via a black-box tool that provides concrete bounds on the expected maximum number of steps needed until local search reaches an exact local optimum. This bound is particularly strong, in the sense that it holds for any starting feasible solution, any choice of pivoting rule, and does not rely on the choice of specific noise distributions that are applied on the input, but it is parameterized by just a global upper bound ϕ on the probability density. The power of this tool can be demonstrated by instantiating it for various PLS-hard problems of interest to derive efficient smoothed running times (as a function of ϕ and the input size). Most notably, we focus on the important local optimization problem of finding pure Nash equilibria in Congestion Games, that has not been studied before from a smoothed analysis perspective. Specifically, we propose novel smoothed analysis models for general and Network Congestion Games, under various representations, including explicit, step-function, and polynomial resource latencies. We study PLS-hard instances of these problems and show that their standard local search algorithms run in polynomial smoothed time. Further applications of our framework to a wide range of additional combinatorial problems can be found in the full version of our paper.
Cite as

Yiannis Giannakopoulos, Alexander Grosz, and Themistoklis Melissourgos. On the Smoothed Complexity of Combinatorial Local Search. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 72:1-72:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{giannakopoulos_et_al:LIPIcs.ICALP.2024.72,
  author =	{Giannakopoulos, Yiannis and Grosz, Alexander and Melissourgos, Themistoklis},
  title =	{{On the Smoothed Complexity of Combinatorial Local Search}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{72:1--72:19},
  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.2024.72},
  URN =		{urn:nbn:de:0030-drops-202154},
  doi =		{10.4230/LIPIcs.ICALP.2024.72},
  annote =	{Keywords: Smoothed Analysis, local search, better-response dynamics, PLS-hardness, combinatorial local optimization, congestion games, pure Nash equilibria}
}
Document
Track C: Foundations of Networks and Multi-Agent Systems: Models, Algorithms and Information Management
DOI: 10.4230/LIPIcs.ICALP.2019.138
Computing Exact Solutions of Consensus Halving and the Borsuk-Ulam Theorem

Authors: Argyrios Deligkas, John Fearnley, Themistoklis Melissourgos, and Paul G. Spirakis

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

Abstract
We study the problem of finding an exact solution to the consensus halving problem. While recent work has shown that the approximate version of this problem is PPA-complete [Filos-Ratsikas and Goldberg, 2018; Filos-Ratsikas and Goldberg, 2018], we show that the exact version is much harder. Specifically, finding a solution with n agents and n cuts is FIXP-hard, and deciding whether there exists a solution with fewer than n cuts is ETR-complete. We also give a QPTAS for the case where each agent’s valuation is a polynomial. Along the way, we define a new complexity class BU, which captures all problems that can be reduced to solving an instance of the Borsuk-Ulam problem exactly. We show that FIXP subseteq BU subseteq TFETR and that LinearBU = PPA, where LinearBU is the subclass of BU in which the Borsuk-Ulam instance is specified by a linear arithmetic circuit.
Cite as

Argyrios Deligkas, John Fearnley, Themistoklis Melissourgos, and Paul G. Spirakis. Computing Exact Solutions of Consensus Halving and the Borsuk-Ulam Theorem. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 138:1-138:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{deligkas_et_al:LIPIcs.ICALP.2019.138,
  author =	{Deligkas, Argyrios and Fearnley, John and Melissourgos, Themistoklis and Spirakis, Paul G.},
  title =	{{Computing Exact Solutions of Consensus Halving and the Borsuk-Ulam Theorem}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{138:1--138:14},
  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.2019.138},
  URN =		{urn:nbn:de:0030-drops-107141},
  doi =		{10.4230/LIPIcs.ICALP.2019.138},
  annote =	{Keywords: PPA, FIXP, ETR, consensus halving, circuit, reduction, complexity class}
}
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