randomized distributed shortest paths algorithms
This paper is concerned with distributed algorithm for finding shortest paths in an asynchronous communication network. For the problem of Breadth First Search, the best previously known algorithms required either &THgr;( V ) time, or &THgr; ( E + V  D ) communication. We present new algorithm, which requires O ( D 1+&egr; ) time, and O ( E 1+&egr; ) messages, for any &egr; > 0. (Here, V is number of nodes, E is number of edges and D is the diameter.) This constitutes a major step towards achieving the lower bounds, which are &OHgr;( E ) communication and &OHgr;( D ) time. For the general (weighted) shortest paths problem, previously known shortest-paths algorithms required O ( k  V 2 ) messages and O ( V  log k V ) time. Our algorithm requires O ( E 1 + &egr;  log W ) messages and O ( V 1 + &egr;  log W ) time. Our results enable to improve significantly solutions for other basic network problems (e.g. leader election).
randomization distributed shortest path algorithm paper distributed algorithms asynchronous communication communication network search timing message lower bound general log