Paper Info
Title
Complexity of determining the most vital elements for the 1-median and 1-center location problems
Abstract
We consider the k most vital edges (nodes) and min edge (node) blocker versions of the 1-median and 1-center location problems. Given a weighted connected graph with distances on edges and weights on nodes, the k most vital edges (nodes) 1-median (respectively 1-center) problem consists of finding a subset of k edges (nodes) whose removal from the graph leads to an optimal solution for the 1-median (respectively 1-center) problem with the largest total weighted distance (respectively maximum weighted distance). The complementary problem, min edge (node) blocker 1-median (respectively 1-center), consists of removing a subset of edges (nodes) of minimum cardinality such that an optimal solution for the 1-median (respectively 1-center) problem has a total weighted distance (respectively a maximum weighted distance) at least as large as a specified threshold. We show that k most vital edges 1-median and k most vital edges 1-center are NP-hard to approximate within a factor 7/5 - ε and 4/3 - ε respectively, for any ε 0, while k most vital nodes 1-median and k most vital nodes 1-center are NP-hard to approximate within a factor 3/2 - ε, for any ε 0. We also show that the complementary versions of these four problems are NP-hard to approximate within a factor 1.36.
Year
Venue
Keywords
2010
conference on combinatorial optimization and applications
1-center location problem,vital element,vital node,vital edge,optimal solution,min edge,vital nodes 1-center,maximum weighted distance,k edge,vital edges 1-center,blocker 1-median,approximation,complexity,connected graph
Field
DocType
Volume
Discrete mathematics,Graph,Combinatorics,Weighted distance,Cardinality,Connectivity,Multiple edges,Mathematics
Conference
6508
ISSN
ISBN
Citations 
0302-9743
3-642-17457-4
5
PageRank 
References 
Authors
0.46
7
3
Name
Order
Citations
PageRank
Cristina Bazgan167962.76
Sonia Toubaline2607.54
Daniel Vanderpooten3115374.66