Approximating Alternative Solutions

Authors:
Michael Krüger;Harald Hempel
Affiliations:
Institut für Informatik, Friedrich-Schiller-Universität Jena, Jena, Germany D-07743;Institut für Informatik, Friedrich-Schiller-Universität Jena, Jena, Germany D-07743
Venue:
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
Year:
2008

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Abstract

We study the approximability of alternative solutions for NP-problems. In particular, we show that approximating the second best solution is in many cases, such as MaxCut, MaxSat, Minimum Steiner Tree, and others, substantially easier than approximating a first solution. We prove that our polynomial-time approximation scheme for the second best solution of Minimum Steiner Treeis optimal. In contrast we also argue that for the problems Minimum Independent Dominating Setand Minimum Traveling Salesperson Problema given optimal solution does not simplify finding a second best solution.