An improved approximation algorithm for requirement cut

Authors:
Anupam Gupta;Viswanath Nagarajan;R. Ravi
Affiliations:
Computer Science Department, Carnegie Mellon University, Pittsburgh, PA 15213, USA;IBM T.J. Watson Research Center, Yorktown Heights, NY 10598, USA;Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA 15213, USA
Venue:
Operations Research Letters
Year:
2010

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Abstract

This note presents improved approximation guarantees for the requirement cut problem: given an n-vertex edge-weighted graph G=(V,E), and g groups of vertices X"1,...,X"g@?V with each group X"i having a requirement r"i between 0 and |X"i|, the goal is to find a minimum cost set of edges whose removal separates each group X"i into at least r"i disconnected components. We give a tight @Q(logg) approximation ratio for this problem when the underlying graph is a tree, and show how this implies an O(logk@?logg) approximation ratio for general graphs, where k=|@?"i"="1^gX"i|@?n.