Direct routing: Algorithms and complexity

Authors:
Costas Busch;Malik Magdon-Ismail;Marios Mavronicolas;Paul Spirakis
Affiliations:
Rensselaer Polytechnic Institute, Department of Computer Science, 110 8th Street, 12180, Troy, NY, USA;Rensselaer Polytechnic Institute, Department of Computer Science, 110 8th Street, 12180, Troy, NY, USA;University of Cyprus, Department of Computer Science, P.O. Box 20537, 110 8th Street, CY-1678, Nicosia, NY, Cyprus;University of Patras, Rion, Department of Computer Engineering and Informatics, P.O. Box 20537, 110 8th Street, 265 00, Patras, NY, Greece and Computer Technology Institute, 61 Riga Fereou Street, ...
Venue:
Algorithmica
Year:
2006

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Abstract

Direct routing is the special case ofbufferless routing whereN packets, once injected into the network, must be delivered to their destinations without collisions. We give a general treatment of three facets of direct routing: 1. Algorithms. We present a polynomial-timegreedy direct algorithm which is worst-case optimal. We improve the bound of the greedy algorithm for special cases, by applying variants of this algorithm to commonly used network topologies. In particular, we obtainnear-optimal routing time for thetree, mesh, butterfly, andhypercube. 2. Complexity. By a reduction from Vertex Coloring, we show that optimal Direct Routing is inapproximable, unless P=NP. 3. Lower Bounds for Buffering. We show that certain direct routing problems cannot be solved efficiently; in order to solve these problems,any routing algorithm needs buffers. We give non-trivial lower bounds on such buffering requirements for general routing algorithms.