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Availability of k-Coterie
May 1993 (vol. 42 no. 5)
pp. 553-558

The distributed k-mutual-exclusion problem (k-mutex problem) is the problem of guaranteeing that at most k processes at a time can enter a critical section at a time in a distribution system. A method proposed for the solution of the distributed mutual exclusion problem (i.e., 1-mutex problem) by D. Barbara and H. Garcia-Molina (1987) is an extension of majority consensus and uses coteries. The goodness of coterie-based 1-mutex algorithm strongly depends on the availability of coterie, and it has been shown that majority coterie is optimal in this sense, provided that: the network topology is a complete graph, the links never fail, and p, the reliability of the process, is at least 1/2. The concept of a k-coterie, an extension of a coterie, is introduced for solving the k-mutex problem, and lower and upper bounds are derived on the reliability p for k-majority coterie, a natural extension of majority coterie, to be optimal, under conditions (1)-(3). For example, when k=3, p must be greater than 0.994 for k-majority coterie to be optimal.

[1] L. Lamport, "Time, clocks, and the ordering of events in a distributed system,"Commun. ACM, vol. 21, no. 7, pp. 558-565, July 1978.
[2] G. Ricart and A. K. Agrawala, "An optimal algorithm for mutual exclusion in computer networks,"Commun. ACM, vol. 24, pp. 9-17, 1981.
[3] G. Ricart and A. K. Agrawala, "Author's response to 'On mutual exclusion in computer networks' by Carvalho and Roucairol,"Commun. ACM, vol. 26, pp. 147-148, Feb. 1983.
[4] I. Suzuki and T. Kasami, "A distributed mutual exclusion algorithm,"ACM Trans. Comput. Syst., vol. 3, no. 4, pp. 344-349, 1985.
[5] M. Maekawa, "A√N algorithm for mutual exclusion in decentralized systems,"ACM Trans. Comput. Syst., vol. 3, no. 2, May 1985.
[6] D. Barbara and H. Garcia-Molina, "The reliability of voting mechanisms,"IEEE Trans. Comput., vol. C-36, no. 10, pp. 1197-1208, Oct. 1987.
[7] K. Raymond, "A tree based algorithm for distributed mutual exclusion,"ACM Trans. Comput. Syst., vol. 7, pp. 61-77, 1989.
[8] M. Mizuno, M. L. Neilsen, and R. Rao, "A token based distributed mutual exclusion algorithm based on quorum agreements," inProc. 11th Int. Conf. Distributed Comput. Syst., May 1991, pp. 361-368.
[9] M. Singhal, "A class of deadlock-free maekawa-type algorithms for mutual exclusion in distributed systems,"Distributed Comput., pp. 131-138, Apr. 1991.
[10] M. Raynal, "A simple taxonomy for distributed mutual exclusion algorithms,"ACM Operating Syst. Rev., vol. 25, pp. 47-50, 1991.
[11] H. Garcia-Molina and D. Barbara, "How to assign votes in a distributed systems,"J. ACM, vol. 32, no. 4, pp. 841-860, Oct. 1985.
[12] H. Kakugawa, S. Fujita, M. Yamashita, and T. Ae, "A protocol for distributedk-mutual exclusion," IEICE Japan, SIG Computation Record COMP91-28, pp. 57-64, June 1991.
[13] K. Raymond, "A distributed algorithm for multiple entries to a critical section,"Inform. Processing Lett., vol. 30, pp. 189-193, Feb. 1989.
[14] P. K. Srimani and R. L. Reddy, "Another distributed algorithm for multiple entries to a critical section,"Inform. Processing Lett., vol. 41, pp. 51-57, Jan. 1992.
[15] S. Fujita, M. Yamashita, and T. Ae, "A non trivial solution of the distributedk-mutual exclusion problem,"ISA '91 Algorithms LNCS 557, 1991.
[16] T. Ibaraki and T. Kameda, "Theory of coteries," CSS/LCCR TR90-09, Simon Fraser Univ., Burnaby, B.C., Canada, 1990.
[17] M. Maekawa, A. E. Oldehoeft, and R. R. Oldehoeft,Operating Systems: Advanced Concepts. Menlo Park, CA: Benjamin/Cummings, 1987.
[18] M. Raynal,Algorithms for Mutual Exclusion. North Oxford Academic, 1886. (Translated by D. Beeson).

Index Terms:
distributed k-mutual-exclusion problem; k-mutex problem; critical section; distribution system; network topology; complete graph; concurrency control; distributed processing; graph theory.
H. Kakugawa, S. Fujita, M. Yamashita, T. Ae, "Availability of k-Coterie," IEEE Transactions on Computers, vol. 42, no. 5, pp. 553-558, May 1993, doi:10.1109/12.223674
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