Approximating Alternative Solutions

  • Michael Krüger
  • Harald Hempel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5092)


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.


Feasible Solution Alternative Solution Steiner Tree Hamiltonian Cycle Satisfying Assignment 
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© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Michael Krüger
    • 1
  • Harald Hempel
    • 1
  1. 1.Institut für InformatikFriedrich-Schiller-Universität JenaJenaGermany

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