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