Fast algorithms for bit-serial routing on a hypercube


Journal Article

In this paper we describe an O(log N)-bit-step randomized algorithm for bit-serial message routing on a hypercube. The result is asymptotically optimal, and improves upon the best previously known algorithms by a logarithmic factor. The result also solves the problem of on-line circuit switching in an O(1)-dilated hypercube (i.e., the problem of establishing edge-disjoint paths between the nodes of the dilated hypercube for any one-to-one mapping). Our algorithm is adaptive and we show that this is necessary to achieve the logarithmic speedup. We generalize the Borodin-Hopcroft lower bound on oblivious routing by proving that any randomized oblivious algorithm on a polylogarithmic degree network requires at least Ω(log2N/log log N) bit steps with high probability for almost all permutations. © 1991 Springer-Verlag New York Inc.

Full Text

Duke Authors

Cited Authors

  • Aiello, WA; Leighton, FT; Maggs, BM; Newman, M

Published Date

  • December 1, 1991

Published In

Volume / Issue

  • 24 / 1

Start / End Page

  • 253 - 271

Electronic International Standard Serial Number (EISSN)

  • 1433-0490

International Standard Serial Number (ISSN)

  • 0025-5661

Digital Object Identifier (DOI)

  • 10.1007/BF02090402

Citation Source

  • Scopus