On the approximability of robust spanning tree problems

Adam Kasperski, Paweł Zieliński
2011 Theoretical Computer Science  
In this paper the minimum spanning tree problem with uncertain edge costs is discussed. In order to model the uncertainty a discrete scenario set is specified and a robust framework is adopted to choose a solution. The min-max, min-max regret and 2-stage min-max versions of the problem are discussed. The complexity and approximability of all these problems are explored. It is proved that the min-max and min-max regret versions with nonnegative edge costs are hard to approximate within O(log 1−ϵ
more » ... n) for any ϵ > 0 unless the problems in NP have quasi-polynomial time algorithms. Similarly, the 2-stage min-max problem cannot be approximated within O(log n) unless the problems in NP have quasipolynomial time algorithms. In this paper randomized LP-based approximation algorithms with performance bound of O(log 2 n) for min-max and 2-stage min-max problems are also proposed.
doi:10.1016/j.tcs.2010.10.006 fatcat:vsyx7ynwj5eqhifkzqob7fggru