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 Tree is optimal. In contrast we also argue that for the problems Minimum Independent Dominating Set and Minimum Traveling Salesperson Problem a given optimal solution does not simplify finding a second best solution. © 2008 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Krüger, M., & Hempel, H. (2008). Approximating alternative solutions. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5092 LNCS, pp. 204–214). https://doi.org/10.1007/978-3-540-69733-6_21
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