Fast algorithms for bit-serial routing on a hypercube
Bill Aiello, Frank Thomson Leighton, Bruce MacDowell Maggs, Mark J. Newman · 1990
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(l)-dilated hypercube (i.e., partitioning the edges of a dilated hypercube so as to realize an arbitrary permutation of point-to-point connections between the nodes).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 oblivious randomized algorithm on a polylogarithmic degree network requires sZ(log' N/log log N) bit steps with high probability for almost all permutations.