Reducing Conflict Resolution Time for Solving Graph Problems in Broadcast Communications

Abstract In this paper, we propose some algorithms to solve the topological ordering problem, the breadth-first search problem and the connected component problem under the broadcast communication model. The basic idea of our algorithms is to divide a graph into several layers. Only after all vertices in one layer are processed, we begin to process the vertices in another layer. Thus, the number of broadcast conflicts is reduced. We also propose a randomized conflict resolution scheme to resolve conflicts. We show that the average time complexity of our algorithms is Θ(n), where n is the number of available processors and also the number of vertices in the graph.

[1]  Robert Metcalfe,et al.  Ethernet: distributed packet switching for local computer networks , 1976, CACM.

[2]  Sartaj Sahni,et al.  Parallel Matrix and Graph Algorithms , 1981, SIAM J. Comput..

[3]  Steven P. Levitan,et al.  Finding an extremum in a network , 1982, ISCA 1982.

[4]  Richard C. T. Lee,et al.  Conflict-Free Sorting Algorithms Under Single-Channel and Multi-Channel Broadcast Communication Models , 1991, ICCI.

[5]  E. Reingold,et al.  Combinatorial Algorithms: Theory and Practice , 1977 .

[6]  Narsingh Deo,et al.  Graph Theory with Applications to Engineering and Computer Science , 1975, Networks.

[7]  Eli Gafni,et al.  Sorting and Selection in Multi-Channel Broadcast Networks , 1985, ICPP.

[8]  Shimon Even,et al.  Graph Algorithms , 1979 .

[9]  Richard C. T. Lee,et al.  Parallel Graph Algorithms Based Upon Broadcast Communications , 1990, IEEE Trans. Computers.

[10]  John Capetanakis,et al.  Tree algorithms for packet broadcast channels , 1979, IEEE Trans. Inf. Theory.

[11]  Steven P. Levitan,et al.  Algorithms for a Broadcast Protocol Multiprocessor , 1982, IEEE International Conference on Distributed Computing Systems.

[12]  Leonard Kleinrock,et al.  Broadcast Communications and Distributed Algorithms , 1986, IEEE Transactions on Computers.

[13]  K. V. S. Ramarao.  Distributed Sorting on Local Area Networks , 1988, IEEE Trans. Computers.

[14]  Ludek Kucera,et al.  Parallel Computation and Conflicts in Memory Access , 1982, Information Processing Letters.

[15]  Pranay Chaudhuri,et al.  Parallel algorithms for analyzing activity networks , 1986, BIT Comput. Sci. Sect..