The complexity of finding most vital arcs and nodes
The complexity of finding most vital arcs and nodes
Approximation algorithms for NP-hard problems
Increasing the weight of minimum spanning trees
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
On Short Paths Interdiction Problems: Total and Node-Wise Limited Interdiction
Theory of Computing Systems
On syntactic versus computational views of approximability
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Complexity of most vital nodes for independent set in graphs related to tree structures
IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
The most vital nodes with respect to independent set and vertex cover
Discrete Applied Mathematics
Efficient determination of the k most vital edges for the minimum spanning tree problem
Computers and Operations Research
Critical edges/nodes for the minimum spanning tree problem: complexity and approximation
Journal of Combinatorial Optimization
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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.