On the Hardness of Approximating Minimum Monopoly Problems

Authors:
S. Mishra;Jaikumar Radhakrishnan;S. Sivasubramanian
Affiliations:
-;-;-
Venue:
FST TCS '02 Proceedings of the 22nd Conference Kanpur on Foundations of Software Technology and Theoretical Computer Science
Year:
2002

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Abstract

We consider inapproximability for two graph optimisation problems called monopoly and partial monopoly. We prove that these problems cannot be approximated within a factor of (1/3 - 驴) ln n and (1/2 - 驴) lnn, unless NP 驴 Dtime(nO(log log n)), respectively. We also show that, if 驴 is the maximum degree in a graph G, then both problems cannot be approximated within a factor of ln 驴-O(ln ln 驴), unless P = NP, though both these problems can be approximated within a factor of ln(驴) + O(1). Finally, for cubic graphs, we give a 1.6154 approximation algorithm for the monopoly problem and a 5/3 approximation algorithm for partial monopoly problem, and show that they are APX-complete.