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

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