ALCOMFT-TR-03-159
|
![ALCOM-FT](../Main/logo_160x41.gif)
|
Martin Gairing, Thomas Lücking, Marios Mavronicolas and Burkhard Monien
Computing Nash Equilibria for Scheduling on Restricted Parallel Links
Paderborn and Cyprus.
Work package 2.
December 2003.
Abstract: We consider the problem of routing n users on m parallel links, under
the restriction that each user may only be routed on a link from a
certain set of allowed links for the user. Thus, the problem is
equivalent to the correspondingly restricted problem of assigning n
jobs to m parallel machines. In a pure Nash equilibrium, no user may
improve its own individual cost (delay) by unilaterally switching to
another link from its set of allowed links. As our main result, we
introduce a polynomial time algorithm to compute from any given
assignment a pure Nash Equilibrium with non-increased makespan. The
algorithm gradually changes a given assignment by pushing unsplittable
user traffics through a network that is defined by the users and the
links. Here, we use ideas from blocking flows. Furthermore, we use
similar techniques as in the generic Preflow-Push algorithm to
approximate a schedule with minimum makespan, gaining an improved
approximation factor of 2-1/w_1 for identical links, where w_1 is the
largest user traffic. We extend this result to related links, gaining
an approximation factor of 2. Our approximation algorithms run in
polynomial time. We close with tight upper bounds on the coordination
ratio for pure Nash Equilibria.
Postscript file: ALCOMFT-TR-03-159.ps.gz (139 kb).
System maintainer Gerth Stølting Brodal <gerth@cs.au.dk>