A highly asynchronous minimum spanning tree protocol

Summary In this paper, we present an efficient distributed protocol for constructing a minimum-weight spanning tree (MST). Gallager, Humblet and Spira [5] proposed a protocol for this problem with time and message complexitiesO(N logN) andO(E+NlogN) respectively. A protocol withO(N) time complexity was proposed by Awerbuch [1]. We show that the time complexity of the protocol in [5] can also be expressed asO((D+d) logN), whereD is the maximum degree of a node andd is a diameter of the MST and therefore this protocol performs better than the protocol in [1] wheneverD+d/logN. We give a protocol which requiresO(min(N, (D+d)logN)) time andO(E+NlogNlogN/loglogN) messages. The protocol constructs a minimum spanning tree by growing disjoint subtrees of the MST (which are referred to asfragments). Fragments having the same minimum-weight outgoing edge are combined until a single fragment which spans the entire network remains. The protocols in [5] and [1] enforce a balanced growth of fragments. We relax the requirement of balanced growth and obtain a highly asynchronous protocol. In this protocol, fast growing fragments combine more often and there-fore speed up the execution. Gurdip Singh received the B. Tech degree in Computer Science from Indian Institute of Technology, New Delhi in 1986 and the M.S. and Ph.D. degrees in Computer Science from State University of New York at Stony Brook in 1989 and 1991 respectively. Since 1991, he has been an Assistant Professor in the Department of Computing and Information Sciences at Kansas State University. His research interest include design and verification of distributed algorithms, communication networks and distributed shared memories. Arthur Bernstein received his PhD in Electrical Engineering from Columbia University. He is currently a professor in the Computer Science Department at the State University of New York at Stony Brook. His research interests center around concurrency in programming and data-base systems.This work was supported by NSF under grants CCR8701671, CCR8901966 and CCR9211621