Minimum Label s-t Cut has Large Integrality Gaps

30 Aug 2019 Zhang Peng Tang Linqing

Given a graph G=(V,E) with a label set L = {l_1, l_2, ..., l_q}, in which each edge has a label from L, a source s in V, and a sink t in V, the Min Label s-t Cut problem asks to pick a set L' subseteq L of labels with minimized cardinality, such that the removal of all edges with labels in L' from G disconnects s and t. This problem comes from many applications in real world, for example, information security and computer networks. In this paper, we study two linear programs for Min Label s-t Cut, proving that both of them have large integrality gaps, namely, Omega(m) and Omega(m^{1/3-epsilon}) for the respective linear programs, where m is the number of edges in the graph and epsilon > 0 is any arbitrarily small constant... (read more)

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