Efficient distributed algorithms for single-source shortest paths and related problems on plane networks

Abstract

An efficient distributed algorithm is given for computing a single-source shortest path tree in an asynchronous planar network. The algorithm has message and time complexity O(pn) on an n-node network, where p is the smallest number of faces needed to cover all the nodes, taken over all possible plane embeddings of the network. The complexity of the algorithm ranges from O(n) to O(n ²) as p ranges from 1 to Θ(n). The algorithm incorporates optimal distributed solutions to a number of interesting subproblems including: (i) decomposing the plane embedding into Θ(p) outerplane graphs with favorable properties; (ii) a single-source algorithm for outerplane graphs; and (iii) identifying any edge in an outerplane graph whose cost exceeds the distance between its endpoints. As an application, an efficient message routing scheme is presented which adapts to changing link conditions and routes along near-shortest paths.

Research supported in part by a grant-in-aid of research from the Graduate School of the University of Minnesota. The first author was also supported in part by NSF grant CCR-8808574. Authors' e-mail addresses: janardan@umn-cs.cs.umn.edu; scheng@umn-cs.cs.umn.edu.