Approximation schemes for the restricted shortest path problem
Mathematics of Operations Research
The hardness of approximation: gap location
Computational Complexity
The complexity of finding most vital arcs and nodes
The complexity of finding most vital arcs and nodes
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
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
A simple linear time algorithm for cograph recognition
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
Complexity of determining the most vital elements for the 1-median and 1-center location problems
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part I
The most vital nodes with respect to independent set and vertex cover
Discrete Applied Mathematics
Complexity of determining the most vital elements for the p-median and p-center location problems
Journal of Combinatorial Optimization
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Given an undirected graph with weights on its vertices, the k most vital nodes independent set problem consists of determining a set of k vertices whose removal results in the greatest decrease in the maximum weight of independent sets. We also consider the complementary problem, minimum node blocker independent set that consists of removing a subset of vertices of minimum size such that the maximum weight of independent sets in the remaining graph is at most a specified value. We show that these problems are NP-hard on bipartite graphs but polynomial-time solvable on unweighted bipartite graphs. Furthermore, these problems are polynomial also on graphs of bounded treewidth and cographs. A result on the non-existence of a ptas is presented, too.