Cut problems and their application to divide-and-conquer
Approximation algorithms for NP-hard problems
Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms
Journal of the ACM (JACM)
Approximate Max-Flow Min-(Multi)Cut Theorems and Their Applications
SIAM Journal on Computing
Short length Menger's theorem and reliable optical routing
Theoretical Computer Science
Algorithms for Fault-Tolerant Routing in Circuit-Switched Networks
SIAM Journal on Discrete Mathematics
Flows over edge-disjoint mixed multipaths and applications
Discrete Applied Mathematics
Single source multiroute flows and cuts on uniform capacity networks
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Algorithms for 2-Route Cut Problems
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Approximation algorithms and hardness of the k-route cut problem
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Approximate duality of multicommodity multiroute flows and cuts: single source case
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
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We study a number of multi-route cut problems: given a graph G = (V, E) and connectivity thresholds k(u, v) on pairs of nodes, the goal is to find a minimum cost set of edges or vertices the removal of which reduces the connectivity between every pair (u, v) to strictly below its given threshold. These problems arise in the context of reliability in communication networks; They are natural generalizations of traditional minimum cut problems where the thresholds are either 1 (we want to completely separate the pair) or ∞ (we don't care about the connectivity for the pair). We provide the first non-trivial approximations to a number of variants of the problem including for both node-disjoint and edge-disjoint connectivity thresholds. A main contribution of our work is an extension of the region growing technique for approximating minimum multicuts to the multi-route setting. When the connectivity thresholds are either 2 or ∞ (the "2-route cut" case), we obtain polylogarithmic approximations while satisfying the thresholds exactly. For arbitrary connectivity thresholds this approach leads to bicriteria approximations where we approximately satisfy the thresholds and approximately minimize the cost. We present a number of different algorithms achieving different cost-connectivity tradeoffs.