Selfish Routing and Path Coloring in All-Optical Networks

Publication Date

January 2007

Document Type

Contribution to a Book

Publication Title

Combinatorial and Algorithmic Aspects of Networking

Editor

Jeannette Janssen, Paweł Prałat

Volume

4852

DOI

10.1007/978-3-540-77294-1_8

First Page

71

Last Page

84

Abstract

We study routing and path coloring problems in all-optical networks as non-cooperative games. We especially focus on oblivious payment functions, that is, functions that charge a player according to her own strategy only.We first strengthen a known relation between such games and online routing and path coloring. In particular, we show that the price of anarchy of such games is lower-bounded by, and in several cases precisely equal to, the competitive ratio of appropriate modifications of the First Fit algorithm.Based on this framework we provide results for two classes of games in ring networks: in Selfish Routing and Path Coloring a player must determine both a routing and a coloring for her request, while in Selfish Path Coloring the routing is predetermined and only a coloring of requests needs to be specified. We prove specific upper and lower bounds on the price of anarchy of these games under various payment functions.

Keywords

Short Path, Nash Equilibrium, Social Cost, Competitive Ratio, Online Algorithm

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