Optimal attack and reinforcement of a network
Journal of the ACM (JACM)
Packing and covering a tree by subtrees
Combinatorica
Finding minimum-cost circulations by successive approximation
Mathematics of Operations Research
The network inhibition problem
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
A polynomial-time simplex method for the maximum k-flow problem
Mathematical Programming: Series A and B
The Complexity of Multiterminal Cuts
SIAM Journal on Computing
On budget-constrained flow improvement
Information Processing Letters
A graph-based system for network-vulnerability analysis
Proceedings of the 1998 workshop on New security paradigms
An improved approximation algorithm for MULTIWAY CUT
Journal of Computer and System Sciences - 30th annual ACM symposium on theory of computing
Approximate Max-Flow Min-(Multi)Cut Theorems and Their Applications
SIAM Journal on Computing
Multiway cuts in node weighted graphs
Journal of Algorithms
Rounding Algorithms for a Geometric Embedding of Minimum Multiway Cut
Mathematics of Operations Research
Optimal 3-terminal cuts and linear programming
Mathematical Programming: Series A and B
Approximating the k-multicut problem
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
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The polynomial-time solvable k-hurdle problem is a natural generalization of the classical s-t minimum cut problem where we must select a minimum-cost subset S of the edges of a graph such that |p ∩ S| ≥ k for every s-t path p. In this paper, we describe a set of approximation algorithms for "k-hurdle" variants of the NP-hard multiway cut and multicut problems. For the k-hurdle multiway cut problem with r terminals, we give two results, the first being a pseudoapproximation algorithm that outputs a (k - 1)-hurdle solution whose cost is at most that of an optimal solution for k hurdles. Secondly, we provide two different 2(1- 1/r)-approximation algorithms. The first is based on rounding the solution of a linear program that embeds our graph into a simplex, and although this same linear program yields stronger approximation guarantees for the traditional multiway cut problem, we show that its integrality gap increases to 2(1 - 1/r) in the k-hurdle case. Our second approximation result is based on half-integrality, for which we provide a simple randomized half-integrality proof that works for both edge and vertex k-hurdle multiway cuts that generalizes the half-integrality results of Garg et al. for the vertex multiway cut problem. For the k-hurdle multicut problem in an n-vertex graph, we provide an algorithm that, for any constant Ɛ 0, outputs a ⌈(1 - Ɛ)k⌉-hurdle solution of cost at most O(log n) times that of an optimal k-hurdle solution, and we obtain a 2-approximation algorithm for trees.