Finding k-cuts within twice the optimal
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
A polynomial algorithm for the k-cut problem for fixed k
Mathematics of Operations Research
The Complexity of Multiterminal Cuts
SIAM Journal on Computing
An improved approximation algorithm for multiway cut
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Approximate Max-Flow Min-(Multi)Cut Theorems and Their Applications
SIAM Journal on Computing
A 2-Approximation Algorithm for the Directed Multiway Cut Problem
SIAM Journal on Computing
Cutting and Partitioning a Graph aifter a Fixed Pattern (Extended Abstract)
Proceedings of the 10th Colloquium on Automata, Languages and Programming
A new and improved algorithm for the 3-cut problem
Operations Research Letters
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Consider a set of users and servers connected by a network. Each server provides a unique service which is of certain benefit to each user. Now comes an attacker, who wishes to destroy a set of edges of the network in the fashion that maximizes his net gain, namely, the total disconnected benefit of users minus the total edge-destruction cost. We first discuss that the problem is polynomially solvable in the single-server case. In the multiple-server case, we will show, the problem is, however, NP-hard. In particular, when there are only two servers, the network disconnection problem becomes intractable. Then a $\frac{3}{2}$-approximation algorithm is developed for the two-server case.