Complexity and approximability issues of Shared Risk Resource Group

This article investigates the consequences of the Shared Risk Ressource Groups (SRRG) model on classical combinatorial concepts of network survivability. It focuses on complexity and approximability issues, and on the evolutions of the relationships among these questions. We introduce a combinatorial model for SRRG based on edge-colored graphs. The notions of colored cut and colored spanning tree are introduced, the hardness and non-approximability of path, cut and spanning tree colored optimization problems are proved. We provide approximation algorithms, and investigate specific polynomial cases. Deep differences between colored combinatorial questions and their counterparts in classical graph theory are shown. In particular, results concerning the relationships among colored problems are presented.

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