On bounded load routings for modeling k-regular connection topologies

Authors:
Adrian Kosowski;Michał Małafiejski;Paweł Żyliński
Affiliations:
Dept. of Algorithms and System Modeling, Gdańsk University of Technology;Dept. of Algorithms and System Modeling, Gdańsk University of Technology;Institute of Mathematics, University of Gdańsk
Venue:
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Year:
2005

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Abstract

The paper deals with the problem of modeling a k-regular topology over an existing network architecture by establishing virtual point-to-point communication paths, referred to as k-routing. We consider the question of the existence and minimisation of edge spread of k-routings with bounded edge load in undirected networks. Efficient algorithms are presented for determining minimal k-routings with edge load 1 and for certain cases with edge load 2. On the negative side, the problems of finding a 6-routing with load 2 and of minimising a 2-routing with load 2 are proven to be NP-hard (though the latter is approximable within 7/6). The results imply the NP-hardness of the well known all-to-all routing problem for bounded edge load.