Paper Info
Title
Primal-dual based distributed algorithms for vertex cover with semi-hard capacities
Abstract
In this paper we consider the weighted, capacitated vertex cover problem with hard capacities (capVC). Here, we are given an undirected graph G=(V,E), non-negative vertex weights wtv for all vertices v ∈ V, and node-capacities Bv ≥ 1 for all v ∈ V. A feasible solution to a given capVC instance consists of a vertex cover C ⊆ V. Each edge e ∈ E is assigned to one of its endpoints in C and the number of edges assigned to any vertex v ∈ C is at most Bv. The goal is to minimize the total weight of C.For a parameter ε0 we give a deterministic, distributed algorithm for the capVC problem that computes a vertex cover C of weight at most (2+ε) • opt where opt is the weight of a minimum-weight feasible solution to the given instance. The number of edges assigned to any node v ∈ C is at most (4+ε)• Bv. The running time of our algorithm is O(log (n W)/ε), where n is the number of nodes in the network and W=wtmax/weightmin is the ratio of largest to smallest weight.This result is complemented by a lower-bound saying that any distributed algorithm for capVC which requires a poly-logarithmic number of rounds is bound to violate the capacity constraints by a factor two.The main feature of the algorithm is that it is derived in a systematic fashion starting from a primal-dual sequential algorithm.
Year
DOI
Venue
2005
10.1145/1073814.1073835
PODC
Keywords
Field
DocType
capvc problem,poly-logarithmic number,primal-dual sequential algorithm,capacitated vertex cover problem,smallest weight,total weight,capvc instance,non-negative vertex weights wtv,semi-hard capacity,node v,vertex v,distributed algorithm,vertex cover,distributed algorithms,approximation algorithms,lower bound
Approximation algorithm,Graph,Discrete mathematics,Combinatorics,Vertex (geometry),Vertex (graph theory),Neighbourhood (graph theory),Distributed algorithm,Vertex cover,Sequential algorithm,Mathematics
Conference
ISBN
Citations 
PageRank 
1-58113-994-2
12
0.64
References 
Authors
18
4
Name
Order
Citations
PageRank
F. Grandoni1120.64
Jochen Könemann21589.98
A. Panconesi3231.28
Mauro Sozio462031.39