An O(log k) Approximate Min-Cut Max-Flow Theorem and Approximation Algorithm
SIAM Journal on Computing
Analysis of multi-path routing
IEEE/ACM Transactions on Networking (TON)
Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms
Journal of the ACM (JACM)
Approximation Algorithms for Disjoint Paths and Related Routing and Packing Problems
Mathematics of Operations Research
Improved bounds for the unsplittable flow problem
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Approximate Max-Flow Min-(Multi)Cut Theorems and Their Applications
SIAM Journal on Computing
Approximation Algorithms for Single-Source Unsplittable Flow
SIAM Journal on Computing
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation Algorithms for the Unsplittable Flow Problem
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
Improved approximations for edge-disjoint paths, unsplittable flow, and related routing problems
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Single-source unsplittable flow
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Routing restorable bandwidth guaranteed connections using maximum 2-route flows
IEEE/ACM Transactions on Networking (TON)
Journal of Computer and System Sciences
Multiroute flow problem
Short length Menger's theorem and reliable optical routing
Theoretical Computer Science
Region growing for multi-route cuts
SODA '10 Proceedings of the twenty-first 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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For an integer h ≥ 1, an elementary h-route flow is a flow along h edge disjoint paths between a source and a sink, each path carrying a unit of flow, and a single commodity h-route flow is a non-negative linear combination of elementary h-flows. An instance of a single source multicommodity flow problem for a graph G = (V, E) consists of a source vertex s ε V and k sinks t1,..., tk ε V; we denote it I = (s; t1,..., tk). In the single source multicommodity multiroute flow problem, we are given an instance I = (s; t1,..., tk) and an integer h ≥ 1, and the objective is to maximize the total amount of flow that is transferred from the source to the sinks so that the capacity constraints are obeyed and, moreover, the flow of each commodity is an h-route flow. We study the relation between classical and multiroute single source flows on networks with uniform capacities and we provide a tight bound. In particular, we prove the following result. Given an instance ≥ = (s; t1,...,tk) such that each s - ti pair is h-connected, the maximum classical flow between s and the ti's is at most 2(1 - 1/h)-times larger than the maximum h-route flow between s and the ti's and this is the best possible bound for h ≥ 2. This, as we show, is in contrast to the situation of general multicommodity multiroute flows that are up to k(1 - 1/h)-times smaller than their classical counterparts. As a corollary, we establish a max-flow min-cut theorem for the single source multicommodity multiroute flow and cut. An h-disconnecting cut for I is a set of edges F ⊆ E such that for each i, the maximum h-flow between s - ti is zero. We show that the maximum h-flow is within 2(h-1) of the mininimum h-disconnecting cut, independently of the number of commodities; we also describe a 2(h - 1)-approximation algorithm for the minimum h-disconnecting cut problem.