Abstract
We present a problem called (m,1,k)-resource allocation to model group mutual exclusion with bounded capacity. Specifically, the problem concerns the scheduling of a resource among m groups of processes. The resource can be used by at most k processes of the same group at a time, but no two processes of different groups can use the resource simultaneously. The problem reduces to group mutual exclusion when k is equal to the group size. We then generalize quorum systems for mutual exclusion to the problem. We show that the study of quorum systems for (m,1,k)-resource allocation is closely related to some classical problems in combinatorics and in finite projective geometries. By applying the results there, we are able to obtain some optimal/near-optimal quorum systems.
Part of this research was done when the author was visiting Lab for Computer Science, Massachusetts Institute of Technology (1999-2000). Research supported in part by the National Science Council, Taiwan, Grants NSC 92-2213-E-002-017.
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Fischer, M.J., Lynch, N.A., Burns, J.E., Borodin, A.: Resource allocation with immunity to limited process failure (preliminary report). In: 20th Annual Symposium on Foundations of Computer Science, pp. 234–254 (1979)
Joung, Y.J.: Asynchronous group mutual exclusion. Distributed Computing 13, 189–206 (2000)
Keane, P., Moir, M.: A simple local-spin group mutual exclusion algorithm. In: Proceedings of the 18th Annual ACM Symposium on Principles of Distributed Computing (PODC), pp. 23–32 (1999)
Hadzilacos, V.: A note on group mutual exclusion. In: Proceedings of the 20th Annual ACM Symposium on Principles of Distributed Computing, PODC (2001)
Maekawa, M.: A \(\sqrt{N}\) algorithm for mutual exclusion in decentralized systems. ACM Transactions on Computer Systems 3, 145–159 (1985)
Barbara, D., Garcia-Molina, H.: Mutual exclusion in partitioned distributed systems. Distributed Computing 1, 119–132 (1986)
Peleg, D., Wool, A.: Crumbling walls: A class of practical and efficient quorum systems. Distributed Computing 10, 87–97 (1997)
Kakugawa, H., Fujita, S., Yamashita, M., Ae, T.: Availability of k-coterie. IEEE Transactions on Computers 42, 553–558 (1993)
Kuo, Y.C., Huang, S.T.: A simple scheme to construct k-coteries with O(\(\sqrt{N}\)) uniform quorum sizes. Information Processing Letters 59, 31–36 (1996)
Neilsen, M.L.: Properties of nondominated K-coteries. Journal of Systems and Software 37, 91–96 (1997)
MacNeish, H.F.: Euler squares. The Annals of Mathematics 2nd series 23, 221–227 (1922)
Neilsen, M.L., Mizuno, M.: Coterie join algorithm. IEEE Transactions on Parallel and Distributed Systems 3, 582–590 (1992)
Malkhi, D., Reiter, M.K., Wool, A.: The load and availability of Byzantine quorum systems. SIAM Journal on Computing 29, 1889–1906 (2000)
Pedoe, D.: An Introduction to Projective geometry (1963)
Hardy, G.H., Wright, E.M.: An introduction to the theory of numbers (1965)
Joung, Y.J.: Quorum-based algorithms for group mutual exclusion. IEEE Transactions on Parallel and Distributed Systems 14, 463–476 (2003)
Garcia-Molina, H., Barbara, D.: How to assign votes in a distributed system. Journal of the ACM 32, 841–860 (1985)
Joung, Y.J.: The congenial talking philosophers problem in computer networks (extended abstract). In: Jayanti, P. (ed.) DISC 1999. LNCS, vol. 1693, pp. 195–209. Springer, Heidelberg (1999)
Wu, K.P., Joung, Y.J.: Asynchronous group mutual exclusion in ring networks. IEE Proceedings–Computers and Digital Techniques 147, 1–8 (2000)
Cantarell, S., Datta, A.K., Petit, F., Villain, V.: Token based group mutual exclusion for asynchronous rings. In: Proceedings of the 21st International Conference on Distributed Computing Systems (ICDCS), pp. 691–694 (2001)
Peleg, D., Wool, A.: The availability of quorum systems. Information and Computation 123, 210–223 (1995)
Naor, M., Wool, A.: The load, capacity, and availability of quorum systems. SIAM Journal on Computing 27, 423–447 (1998)
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Joung, YJ. (2004). On Quorum Systems for Group Resources with Bounded Capacity. In: Guerraoui, R. (eds) Distributed Computing. DISC 2004. Lecture Notes in Computer Science, vol 3274. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30186-8_7
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DOI: https://doi.org/10.1007/978-3-540-30186-8_7
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