Abstract
We propose two simple algorithms based on bounded tickets for the mutual exclusion problem. These are modifications of the Bakery algorithm. An unattractive property of the Bakery algorithm is that the shared memory size is unbounded. The first algorithm based on bounded tickets uses one extra process that does not correspond to any user. It is lockout-free and mutual exclusion on the asynchronous single-writer/multi-reader shared memory model. We then modify it to reduce the shared memory size with the cost of another extra process. The maximum waiting time using each of them is bounded by (n − 1)c + O(nl), where n is the number of users, l is an upper bound on the time between two successive atomic steps, and c is an upper bound on the time that any user spends using the resource. The shared memory size needed by the first algorithm and the second algorithm are (n + 1)(1+⌈log(2n+ l)⌉) bits and n(2 + ⌈logn⌉) + 2 bits, respectively.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
U. Abraham, “Bakery Algorithms”, Technical Report, Dept. of Mathematics, Ben Gurion University, Beer-Sheva, Israel, May 2001.
J.H. Anderson, “Lamport on mutual exclusion: 27 years of planting seeds”, Proceedings of the 27th Annual ACM Symposium on Principles of Distributed Computing, Newport, Rhode Island, pp.3–12, 2001.
H. Attiya and J. Welch, “Distributed Computing: Fundamentals, Simulations and Advanced Topics”, McGraw-Hill, New York, 1998.
J.E. Burns, “Mutual exclusion with linear waiting using binary shared variables”, ACM SIGACT News, vol.10, pp.42–47, 1978.
J.E. Burns, P. Jackson, N.A. Lynch, M.J. Fischer, and G.L. Peterson, “Data requirements for implementation of N-process mutual exclusion using a single shared variable”, J. of the ACM, vol.29, pp.183–205, 1982.
J.E. Burns, and N.A. Lynch, “Bounds on shared memory for mutual exclusion”, Information and Computation, vol.107, pp.171–184, 1993.
A.B. Cremers and T.N. Hibbard, “Mutual exclusion of N processors using an O(N)-valued message variable”, 5th International Colloquium on Automata, Languages and Programming, Udine, Italy, Lecture Notes in Computer Science, vol.62, pp.165–176, 1978.
E.W. Dijkstra, “Solution of a problem in concurrent programming control”, Communications of the ACM, vol.8, p.569, 1965.
D. Dolev and N. Shavit, “Bounded concurrent time-stamping”, SIAM J. on Computing, vol.26, pp.418–455, 1997.
M.J. Fischer, N.A. Lynch, J.E. Burns, and A. Borodin, “Distributed FIFO allocation of identical resources using small shared space”, ACM Transactions on Programming Languages and Systems, vol.11, pp.90–114, 1989.
Y. Igarashi, H. Kurumazaki, and Y. Nishitani, “Some modifications of the tournament algorithm for the mutual exclusion problem”, IEICE Transactions on Information and Systems, vol.E.82-D, pp.368–375, 1999.
Y. Igarashi and Y. Nishitani, “Speedup of the n-process mutual exclusion algorithm”, Parallel Processing Letters, vol.9, pp.475–485, 1999.
P. Jayanti, K. Tan, G. Friedland, and A. Katz, “Bounded Lamport’s bakery algorithm”, Proceedings of SOFTSEM’2001, Lecture Notes in Computer Science, vol.2234, Springer-Verlag, Berlin, pp.261–270, November 2001.
L. Lamport, “A new solution of Dijkstra’s concurrent programming problem”, Communications of ACM, vol.17, pp.453–455, 1974.
L. Lamport, “The mutual exclusion problem. Part II: Statement and solutions”, J. of the ACM, vol.33, pp.327–348, 1986.
L. Lamport, “A fast mutual exclusion algorithm”, ACM Transactions on Computer Systems, vol.5, pp.1–11, 1987.
N.A. Lynch, “Distributed Algorithms”, Morgan Kaufmann, San Francisco, California, 1996.
G.L. Peterson, “Myths about the mutual exclusion problem”, Information Processing Letters, vol.12, pp.115–116, 1981.
G.L. Peterson and M.J. Fischer, “Economical solutions for the critical section problem in a distributed system”, Proceedings of the 9th Annual ACM Symposium on Theory of Computing, Boulder, Colorado, pp.91–97, 1977.
M. Takamura and Y. Igarashi, “A simplification of the Bakery algorithm based on bounded tickets for the mutual exclusion problem”, Technical Report of IEICE, vol.101, no.376, COMP2001-45, pp.61–68, October 2001.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Takamura, M., Igarashi, Y. (2002). Simple Mutual Exclusion Algorithms Based on Bounded Tickets on the Asynchronous Shared Memory Model. In: Ibarra, O.H., Zhang, L. (eds) Computing and Combinatorics. COCOON 2002. Lecture Notes in Computer Science, vol 2387. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45655-4_29
Download citation
DOI: https://doi.org/10.1007/3-540-45655-4_29
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43996-7
Online ISBN: 978-3-540-45655-1
eBook Packages: Springer Book Archive