Efficient Algorithms for the Label Cut Problems

Abstract

Given a graph with labels defined on edges and a source-sink pair (s, t), the Label s-t Cut problem asks a minimum number of labels such that the removal of edges with these labels disconnects s and t. Similarly, the Global Label Cut problem asks a minimum number of labels such that its removal disconnects G itself. For these two problems we give some efficient algorithms that are useful in practice. In particular, we give a combinatorial l max -approximation algorithm for the Label s-t Cut problem, where l max is the maximum s-t length. We show the Global Label Cut problem is polynomial-time solvable in several special cases, including graphs with bounded treewidth, planar graphs, and instances with bounded label frequency.