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An Efficient Distributed Protocol for Finding Shortest Paths in Networks with Negative Weights
May 1989 (vol. 15 no. 5)
pp. 639-644

The design is discussed of distributed algorithms for the single-source shortest-path problem to run on an asynchronous directed network in which some of the edges may be associated with negative weights, and thus in which a cycle of negative total weight may also exist. The only existing solution in the literature for this problem is due to K.M. Chandy and J. Misra (1982), and it has, in the worst case, an unbounded message complexity. A synchronous version of the Chandy-Misra algorithm is described and studied, and it is proved that for a network with m edges and n nodes, the worst case message and time complexities of this algorithm are O(mn) and O(n), respectively. This algorithm is then combined with an efficient synchronizer to yield an asynchronous protocol that retains the same message and time complexities.

[1] B. Awerbuch, "Complexity of network synchronization,"J. ACM, vol. 32, no. 4, pp. 804-823, Oct. 1985.
[2] B. Awerbuch, "Reducing complexities in the distributed max-flow and breadth-first-search algorithms by means of network synchronization,"Networks, vol. 15, pp. 425-437, 1985.
[3] D. Bersekas and R. Gallager,Data Networks. Englewood Cliffs, NJ: Prentice-Hall, 1987.
[4] D. Bertsekas and J. Eckstein, "Distributed asynchronous relaxation methods for linear network flow problems," inProc. IFAC '87. Oxford, UK: Pergamon, 1987.
[5] K. M. Chandy and J. Misra, "A computation on graphs: Shortest path algorithms,"Commun. ACM, vol. 25, no. 11, pp. 833-837, Nov. 1982.
[6] E. J. H. Chang, "Decentralized algorithms in distributed systems," Ph.D. dissertation, Univ. Toronto, Toronto, Ont., Canada, 1979; also, Tech. Rep. CSRG-103.
[7] M. A. Comeau, K. Thulasiraman, and K. B. Lakshmanan, "An efficient asynchronous distributed protocol to test feasibility of the dual transshipment problem," inProc. 25th Annu. Allerton Conf. Commun., Contr., Comput., Urbana, IL, Sept. 30-Oct. 2, 1987.
[8] N. Deo and C. Y. Pang, "Shortest path algorithms: Taxonomy and annotation,"Networks, vol. 14, no. 2, pp. 275-323, 1984.
[9] E. W. Dijkstra and C. S. Scholten, "Termination detection for diffusing computations,"Inform. Processing Lett., vol. 11, no. 1, pp. 1-4, Aug. 1980.
[10] S. Even,Graph Algorithms. Rockville, MD: Computer Science Press, 1979.
[11] G. N. Frederickson, "A single-source shortest path algorithm for planar distributed network," inProc. STACS 85(Lecture Notes Comput. Sci., Vol. 182). Berlin: Springer-Verlag, 1985, pp. 143-150.
[12] A. V. Goldberg and R. E. Tarjan, "Solving minimum-cost flow problems by successive approximations," inProc. 19th ACM Symp. Theory of Comput., New York, May 25-27, 1987, pp. 7-18.
[13] E. Korach, D. Rotem, and N. Santoro, "Distributed algorithms for finding centers and medians in networks,"ACM Trans. Programming Lang. Syst., vol. 6, no. 3, pp. 380-401, July 1984.
[14] K. B. Lakshmanan, N. Meenakshi, and K. Thulasiraman, "A time-optimal, message-efficient distributed algorithm for depth-first-search,"Inform. Processing Lett., vol. 25, no. 2, pp. 103-109, May 1987.
[15] K. B. Lakshmanan and K. Thulasiraman, "On the use of synchronizers for asynchronous communication networks," inProc. 2nd Int. Workshop Distrib. Algorithms, Amsterdam, The Netherlands, July 8- 10, 1987.
[16] A. Segall, "Distributed network protocols,"IEEE Trans. Inform. Theory, vol. IT-29, pp. 23-25, Jan. 1983.
[17] P. Spirakis and A. Tsakalidis, "A very fast, practical algorithm for finding a negative cycle in a digraph," inProc. ICALP 86(Lecture Notes Comput. Sci., Vol. 226). Berlin, West Germany: Springer-Verlag, 1986, pp. 397-406.

Index Terms:
efficient distributed protocol; negative weights; distributed algorithms; single-source shortest-path problem; asynchronous directed network; edges; cycle; worst case; unbounded message complexity; synchronous version; Chandy-Misra algorithm; nodes; time complexities; efficient synchronizer; asynchronous protocol; computational complexity; directed graphs; distributed processing; protocols
Citation:
K.B. Lakshmanan, K. Thulasiraman, M.A. Comeau, "An Efficient Distributed Protocol for Finding Shortest Paths in Networks with Negative Weights," IEEE Transactions on Software Engineering, vol. 15, no. 5, pp. 639-644, May 1989, doi:10.1109/32.24713
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