Improved guarantees for tree cut sparsifiers

Abstract

Harrelson, Hildrum and Rao [11] construct for a given graph a single tree that acts as a flow sparsifier, i.e., it can approximate multicommodity flows in G up to an O(log 2 nloglog n) factor. Many applications that use these trees do not actually require a flow sparsifier but would already work with just having a cut sparsifier. We show how to construct a cut sparsifier that is a single tree and has quality O(log 1.5 nloglog n). In addition we show a close connection of this problem to the Mincut Linear Arrangement Problem which shows that improving the guarantee to o(log 1.5 n) might be difficult. © 2014 Springer-Verlag Berlin Heidelberg.