Tech Report CS-03-04

On the Complexity of the Robust Spanning Tree Problem with Interval Data

Ionut Aron and Pascal Van Hentenryck

March 2003

Abstract:

This paper studies the complexity of the robust spanning tree problem with interval data (RSTID). It settles the conjecture of Kouvelis by proving that the problem is NP-complete. The paper also shows that the problem remains NP-complete for (1) complete graphs and (2) when the cost intervals are all [0,1]. The proofs of the results show that the difficulty of the RSTID problem resides in two distinct aspects of the problem: the topology of the graph and the numerical properties of the cost intervals. As a consequence, the results suggest new directions for improving and evaluating existing search algorithms for the RSTID problem, since they have only focused on one of these aspects.

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