eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-06-29
50:1
50:19
10.4230/LIPIcs.ICALP.2020.50
article
Node-Max-Cut and the Complexity of Equilibrium in Linear Weighted Congestion Games
Fotakis, Dimitris
1
https://orcid.org/0000-0001-6864-8960
Kandiros, Vardis
2
Lianeas, Thanasis
1
Mouzakis, Nikos
1
Patsilinakos, Panagiotis
1
Skoulakis, Stratis
3
National Technical University of Athens, Greece
Massachusetts Institute of Technology, Cambridge, MA, USA
Singapore University of Technology and Design, Singapore
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol168-icalp2020/LIPIcs.ICALP.2020.50/LIPIcs.ICALP.2020.50.pdf
PLS-completeness
Local-Max-Cut
Weighted Congestion Games
Equilibrium Computation