License: 
Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2020.50
URN: urn:nbn:de:0030-drops-124573
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12457/
Fotakis, Dimitris ;
Kandiros, Vardis ;
Lianeas, Thanasis ;
Mouzakis, Nikos ;
Patsilinakos, Panagiotis ;
Skoulakis, Stratis
Node-Max-Cut and the Complexity of Equilibrium in Linear Weighted Congestion Games
Abstract
In this work, we seek a more refined understanding of the complexity of local optimum computation for Max-Cut and pure Nash equilibrium (PNE) computation for congestion games with weighted players and linear latency functions. We show that computing a PNE of linear weighted congestion games is PLS-complete either for very restricted strategy spaces, namely when player strategies are paths on a series-parallel network with a single origin and destination, or for very restricted latency functions, namely when the latency on each resource is equal to the congestion. Our results reveal a remarkable gap regarding the complexity of PNE in congestion games with weighted and unweighted players, since in case of unweighted players, a PNE can be easily computed by either a simple greedy algorithm (for series-parallel networks) or any better response dynamics (when the latency is equal to the congestion). For the latter of the results above, we need to show first that computing a local optimum of a natural restriction of Max-Cut, which we call Node-Max-Cut, is PLS-complete. In Node-Max-Cut, the input graph is vertex-weighted and the weight of each edge is equal to the product of the weights of its endpoints. Due to the very restricted nature of Node-Max-Cut, the reduction requires a careful combination of new gadgets with ideas and techniques from previous work. We also show how to compute efficiently a (1+ε)-approximate equilibrium for Node-Max-Cut, if the number of different vertex weights is constant.
BibTeX - Entry
@InProceedings{fotakis_et_al:LIPIcs:2020:12457,
author = {Dimitris Fotakis and Vardis Kandiros and Thanasis Lianeas and Nikos Mouzakis and Panagiotis Patsilinakos and Stratis Skoulakis},
title = {{Node-Max-Cut and the Complexity of Equilibrium in Linear Weighted Congestion Games}},
booktitle = {47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
pages = {50:1--50:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-138-2},
ISSN = {1868-8969},
year = {2020},
volume = {168},
editor = {Artur Czumaj and Anuj Dawar and Emanuela Merelli},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2020/12457},
URN = {urn:nbn:de:0030-drops-124573},
doi = {10.4230/LIPIcs.ICALP.2020.50},
annote = {Keywords: PLS-completeness, Local-Max-Cut, Weighted Congestion Games, Equilibrium Computation}
}
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Keywords: |
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PLS-completeness, Local-Max-Cut, Weighted Congestion Games, Equilibrium Computation |
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Collection: |
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47th International Colloquium on Automata, Languages, and Programming (ICALP 2020) |
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Issue Date: |
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2020 |
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Date of publication: |
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29.06.2020 |
