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# Approximability of 3- and 4-hop bounded disjoint paths problems

## Bley, Andreas; Neto, Jose

## Preprint-Reihe des Instituts fÃ¼r Mathematik, Technische UniversitÃ¤t Berlin

A path is said to be l-bounded if it contains at most l edges. We consider two types of l-bounded disjoint paths problems. In the maximum edge- or node-disjoint path problems MEDP(l) and MNDP(l), the task is to find the maximum number of edge- or node-disjoint l-bounded (s,t)-paths in a given graph G with source s and sink t, respectively. In the weighted edge- or node-disjoint path problems WEDP(l) and WNDP(l), we are also given an integer k and non-negative edge weights, and seek for a minimum weight subgraph of G that contains k edge- or node-disjoint l-bounded (s,t)-paths. Both problems are of great practical relevance in the planning of fault-tolerant communication networks, for example.