Constant Time Dynamic Programming on Directed Reconfigurable Networks

ÐSeveral dynamic programming algorithms are considered which can be efficiently implemented using parallel networks with reconfigurable buses. The bit model of general reconfigurable meshes with directed links, common write, and unit-time delay for broadcasting is assumed. Given two sequences of length m and n, respectively, their longest common subsequence can be found in constant time by an O…mh† O…nh† directed reconfigurable mesh, where h ˆ minfm;ng ‡ 1. Moreover, given an n-node directed graph G ˆ …V ;E† with (possibly negative) integer weights on its arcs, the shortest distances from a source node v 2 V to all other nodes can be found in constant time by an O…n2w† O…n2w† directed reconfigurable mesh, where w is the maximum arc weight. Index TermsÐReconfigurable architectures, directed links, dynamic programming, longest common subsequence, shortest paths,