The robust recoverable spanning tree problem with interval costs is polynomially solvable

TL;DR

This paper proves that the robust recoverable spanning tree problem with interval costs can be solved in polynomial time using an iterative relaxation method, and extends this approach to related matroid basis problems.

Contribution

It demonstrates polynomial solvability of the robust recoverable spanning tree problem with interval costs and generalizes the method to matroid basis problems.

Findings

Polynomial algorithms for the robust recoverable spanning tree problem.

Polynomial algorithms for the robust recoverable matroid basis problem.

The iterative relaxation method effectively solves these problems.

Abstract

In this paper the robust recoverable spanning tree problem with interval edge costs is considered. The complexity of this problem has remained open to date. It is shown that the problem is polynomially solvable, by using an iterative relaxation method. A generalization of this idea to the robust recoverable matroid basis problem is also presented. Polynomial algorithms for both robust recoverable problems are proposed.