TY - CHAP

T1 - Direct routing

T2 - Algorithms and complexity

AU - Busch, Costas

AU - Magdon-Ismail, Malik

AU - Mavronicolas, Marios

AU - Spirakis, Paul

N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2004

Y1 - 2004

N2 - Direct routing is the special case of bufferless routing where N packets, once injected into the network, must be routed along specific paths to their destinations without conflicts. We give a general treatment of three facets of direct routing: (i) Algorithms. We present a polynomial time greedy algorithm for arbitrary direct routing problems which is worst-case optimal, i.e., there exist instances for which no direct routing algorithm is better than the greedy. We apply variants of this algorithm to commonly used network topologies particular, we obtain near-optimal routing time for the tree and d-dimensional mesh, given arbitrary sources and destinations; for the butterfly and the hypercube, the same result holds for random destinations. (ii) Complexity. By a reduction from Vertex Coloring, we show that Direct Routing is inapproximable, unless P=NP. (iii) Lower Bounds for Buffering. We show that certain direct routing problems cannot be solved efficiently; to solve these problems, any routing algorithm needs buffers. We give non-trivial lower bounds on such buffering requirements for general routing algorithms.

AB - Direct routing is the special case of bufferless routing where N packets, once injected into the network, must be routed along specific paths to their destinations without conflicts. We give a general treatment of three facets of direct routing: (i) Algorithms. We present a polynomial time greedy algorithm for arbitrary direct routing problems which is worst-case optimal, i.e., there exist instances for which no direct routing algorithm is better than the greedy. We apply variants of this algorithm to commonly used network topologies particular, we obtain near-optimal routing time for the tree and d-dimensional mesh, given arbitrary sources and destinations; for the butterfly and the hypercube, the same result holds for random destinations. (ii) Complexity. By a reduction from Vertex Coloring, we show that Direct Routing is inapproximable, unless P=NP. (iii) Lower Bounds for Buffering. We show that certain direct routing problems cannot be solved efficiently; to solve these problems, any routing algorithm needs buffers. We give non-trivial lower bounds on such buffering requirements for general routing algorithms.

UR - http://www.scopus.com/inward/record.url?scp=26944450181&partnerID=8YFLogxK

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U2 - 10.1007/978-3-540-30140-0_14

DO - 10.1007/978-3-540-30140-0_14

M3 - Chapter

AN - SCOPUS:26944450181

SN - 3540230254

SN - 9783540230250

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 134

EP - 145

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

A2 - Albers, Susanne

A2 - Radzik, Tomasz

PB - Springer Verlag

ER -