This Article 
 Bibliographic References 
 Add to: 
Repeated Computation of Global Functions in a Distributed Environment
August 1994 (vol. 5 no. 8)
pp. 823-834

In a distributed system, many algorithms need repeated computation of a global function.These algorithms generally use a static hierarchy for gathering the necessary data fromall processes. As a result, they are unfair to processes at higher levels of the hierarchy,which have to perform more work than processes at lower levels do. In this paper, wepresent a new revolving hierarchical scheme in which the position of a process in thehierarchy changes with time. This reorganization of the hierarchy is achieved concurrently with its use. It results in algorithms that are not only fair to all processes but also less expensive in terms of messages. The reduction in the number of messages is achieved by reusing messages for more than one computation of the global function. The technique is illustrated for a distributed branch-and-bound problem and for asynchronous computation of fixed points.

[1] Selim G. Akl,The Design and Analysis of Parallel Algorithms. Englewood Cliffs, NJ: Prentice-Hall, 1989.
[2] J.-C. Bermond, J-C. Konig, and M. Raynal, "General and efficient decentralized consensus protocols." inProc. 2nd Int. Workshop on Distributed Algorithms on Graphs, 1987.
[3] J.-C. Bermond, J-C. Konig, and M. Raynal, "General and efficient decentralized consensus protocols." inProc. 2nd Int. Workshop on Distributed Algorithms on Graphs, 1987.
[4] D. P. Bertsekas and J. N. Tsitsiklis,Parallel and Distributed Computations. Englewood Cliffs, NJ: Prentice-Hall, 1989.
[5] L. Bouge, "Repeated snapshots in distributed systems with synchronous communication and their implementation in CSP,"Theoretical Comput. Sci., vol. 49, pp. 145-169, 1987.
[6] K. M. Chandy and L. Lamport, "Distributed snapshots: Determining global states of distributed systems,"ACM Trans. Comput. Syst., vol. 3, no. 1, pp. 63-75, Feb. 1985.
[7] K. M. Chandy, J. Misra, and L. M. Haas, "Distributed deadlock detection,"ACM Trans. Comput. Syst., vol. 1, no. 2, pp. 144-156, May 1983.
[8] E. W. Dijkstra, W. H. J. Feijen, and A. J. M. Van Gasteren, "Derivation of a termination detection algorithm for distributed computation,"Inform. Processing Lett., vol. 16, pp. 217-219, June 1983.
[9] R. A. Finkel and J. P. Fishburn, "Parallelism in alpha-beta search,"Artificial Intell., vol. 19, pp. 89-106, 1982.
[10] V. K. Garg and J. Ghosh, "Symmetry in spite of hierarchy,"Proc. 10th IEEE Int. Conf. Distrib. Computing Syst., 1990, pp. 4-11.
[11] R. Gussella, "Tempo: A clock synchronization algorithm," Tech. Rep., Comput. Sci. Div., Univ. of California, Berkeley, 1986.
[12] I. N. Herstein,Topics in Algebra. New York: Wiley Eastern Ltd., 1975.
[13] T. V. Lakshman and A. K. Agrawala, "Efficient decentralized consensus protocols,"IEEE Trans. Software Eng., vol. SE-12, no. 5, pp. 600-607, May 1986.
[14] G. Le Lann, "Distributed systems: Toward a formal approach,"Proc. AFIP Congress 77, 1977, pp. 155-160.
[15] D. Menasce and R. R. Muntz, "Locking and deadlock detection in distributed data bases,"IEEE Trans. Software Eng., vol. SE-5, no. 3, pp. 195-202, May 1979.
[16] M. L. Powell and D. L. Presotto, "Publishing: A reliable broadcast communication mechanism," inProc. 9th ACM Symp. Operat. Syst. Principles, Oct. 1983, pp. 100-109.
[17] M. J. Quinn,Designing Efficient Algorithms for Parallel Computers. New York: McGraw-Hill, 1989.
[18] J. F. Shoch and J. A. Hupp, "The 'Worm' programs--early experience with a distributed computation,"Commun. ACM, vol. 25, no. 3, pp. 172-180, Mar. 1982.
[19] G. Tel, "Total algorithms,"Parallel and Distrib. Algorithms, Int. Workshop. Amsterdam, the Netherlands: North-Holland, 1989, pp. 187-198.
[20] W. T. Tsai, "The design and maintenance of large hierarchical networks," Ph.D. dissertation, Univ. of California, Berkeley, 1985.
[21] A. M. Van Tilborg and L. D. Wittie, "Wave scheduling: Distributed allocation of task forces in network computers,"Proc. 2nd IEEE Int. Conf. Distrib. Computing Syst., 1981, pp. 337-347.

Index Terms:
Index Termsdistributed algorithms; hierarchical systems; function evaluation; repeated computation; global functions; distributed environment; hierarchy reorganization; revolving hierarchical scheme; fairness; message reduction; message reuse; distributed branch-and-bound problem; asynchronous computation; fixed points; distributed programs; permutations
V.K. Garg, J. Ghosh, "Repeated Computation of Global Functions in a Distributed Environment," IEEE Transactions on Parallel and Distributed Systems, vol. 5, no. 8, pp. 823-834, Aug. 1994, doi:10.1109/71.298209
Usage of this product signifies your acceptance of the Terms of Use.