Recoverable robust spanning tree problem under interval uncertainty representations

TL;DR

This paper introduces a polynomial-time combinatorial algorithm for the recoverable robust spanning tree problem under interval uncertainty, generalizing previous incremental spanning tree solutions and providing approximation results under various uncertainty models.

Contribution

The paper presents the first polynomial-time algorithm for the recoverable robust spanning tree problem under interval uncertainty, extending existing models and offering approximation guarantees.

Findings

Polynomial-time algorithm for recoverable robust spanning tree problem.

Extension of the algorithm to various uncertainty representations.

Approximation results under Bertsimas and Sim uncertainty models.

Abstract

This paper deals with the recoverable robust spanning tree problem under interval uncertainty representations. A polynomial time, combinatorial algorithm for the recoverable spanning tree problem is first constructed. This problem generalizes the incremental spanning tree problem, previously discussed in literature. The algorithm built is then applied to solve the recoverable robust spanning tree problem, under the traditional interval uncertainty representation, in polynomial time. Moreover, the algorithm allows to obtain, under some mild assumptions about the uncertainty intervals,several approximation results for the recoverable robust spanning tree problem under the Bertsimas and Sim interval uncertainty representation and the interval uncertainty representation with a budget constraint.