Approximating max-min linear programs with local algorithms

A local algorithm is a distributed algorithm where each node must operate solely based on the information that was available at system startup within a constant-size neighbourhood of the node. We study the applicability of local algorithms to max-min LPs where the objective is to maximise min k Sigm...

Full description

Saved in:
Bibliographic Details
Published in:2008 IEEE International Symposium on Parallel and Distributed Processing pp. 1 - 10
Main Authors: Floreen, P., Kaski, P., Musto, T., Suomela, J.
Format: Conference Proceeding
Language:English
Published: IEEE 01.04.2008
Subjects:
Algorithm design and analysis
Approximation algorithms
Circuits
Communication networks
Computational modeling
Computer science
Distributed algorithms
Distributed decision making
Information technology
Linear approximation
ISBN:1424416930, 9781424416936
ISSN:1530-2075
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:A local algorithm is a distributed algorithm where each node must operate solely based on the information that was available at system startup within a constant-size neighbourhood of the node. We study the applicability of local algorithms to max-min LPs where the objective is to maximise min k Sigmav CkvXv subject to Sigma v alphaivXv les 1 far each i and Xv ges 0 far each v. Here c kv ges 0, and the support sets V i = {v : alphaiv> 0}, V k = {v : c kv > 0}, I v = {i: alpha iv > 0} and K v = {k : C kv > 0} have bounded size. In the distributed setting, each agent v is responsible for choosing the value of X v , and the communication network is a hypergraph H where the sets V k and V i constitute the hyperedges. We present inapproximability results for a wide range of structural assumptions; for example, even if |V i | and |V k | are bounded by some constants larger than 2, there is no local approximation scheme. To contrast the negative results, we present a local approximation algorithm which achieves good approximation ratios if we can bound the relative growth of the vertex neighbourhoods in H.
ISBN:1424416930
9781424416936
ISSN:1530-2075
DOI:10.1109/IPDPS.2008.4536235