On the connectivity preserving minimum cut problem

Authors:
Qi Duan;Jinhui Xu
Affiliations:
Department of Software and Information Systems, University of North Carolina at Charlotte, Charlotte, NC 28223, USA;Department of Computer Science and Engineering, State University of New York at Buffalo, Buffalo, NY 14260, USA
Venue:
Journal of Computer and System Sciences
Year:
2014

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Abstract

In this paper, we study a generalization of the classical minimum cut problem, called Connectivity Preserving Minimum Cut (CPMC) problem, which seeks a minimum cut to separate a pair (or pairs) of source and destination nodes and meanwhile ensure the connectivity between the source and its partner node(s). For this problem, we consider two variants, connectivity preserving minimum node cut (CPMNC) and connectivity preserving minimum edge cut (CPMEC). For CPMNC, we show that it cannot be approximated within @alogn for some constant @a unless P=NP, and cannot be approximated within any poly(logn) unless NP has quasi-polynomial time algorithms. The hardness results hold even for graphs with unit weight and bipartite graphs. For CPMEC, we show that it is in P for planar graphs.