Approximation Algorithms for Multicommodity-Type Problems with Guarantees Independent of the Graph Size

— Linial, London and Rabinovich [16] and Aumann and Rabani [3] proved that the min-cut max-flow ratio for general maximum concurrent flow problems (when there are k commodities) is O(log k). Here we attempt to derive a more general theory of Steiner cut and flow problems, and we prove bounds that are poly-logarithmic in k for a much broader class of multicommodity flow and cut problems. Our structural results are motivated by the meta question: Suppose we are given a poly(log n) approximation algorithm for a flow or cut problem - when can we give a poly(log k) approximation algorithm for a generalization of this problem to a Steiner cut or flow problem? Thus we require that these approximation guarantees be independent of the size of the graph, and only depend on the number of commodities (or the number of terminal nodes in a Steiner cut problem). For many natural applications (when k = no(1) ) this yields much stronger guarantees. We construct vertex-sparsifiers that approxim...

• Type: Conference
• Year: 2009
• Where: FOCS
• Authors: Ankur Moitra
• Keywords: Approximation Algorithms, Cut Problem, FOCS 2009, Steiner Cut, Theoretical Computer Science