Abstract
The page migration problem is the management problem for a globally addressed shared memory in a multiprocessor system. Each physical page of memory is located at a given processor, and memory references to that page by other processors incur a cost equal to the network distance. At times the page may migrate between processors, at a cost equal to the distance times the page size factor, D. The problem is to schedule movements on-line so as to minimize the total cost of memory references. We consider the problem under the restriction that movement can only occur after a request has been served and before the next request is known. The major results are: we give randomized (2+1/2D)-competitive on-line algorithms for trees (and products of trees, including the hypercube), and for a uniform space when D=1,2. We show that these algorithms are optimal. We prove a 85/27 lower bound on the competitiveness constant of a deterministic algorithm (in arbitrary spaces) with D=1, disproving a conjecture by Black and Sleator. We show a deterministic (2+1/2D)-competitive algorithm for continuous trees. Our analysis is based on work functions, which provide a systematic approach to many competitive analysis problems.
Research partially supported by NSF grant CCR-9112067.
Research partially supported by NSF grant CCR-8958528.
Research partially supported by NSF grant CCR-9009753.
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References
B. Awerbuch, Y. Bartal and A. Fiat. Competitive distributed file allocation. Proc. of 25th Symposium on Theory of Computation, 1993, pages 164–173.
P. Berman, H. J. Karloff, and G. Tardos. A competitive three-server algorithm. In Proc. 1st ACM-SIAM Symp. on Discrete Algorithms, pages 280–290, 1990.
D. Black, A. Gupta, and W. Weber. Competitive management of distributed shared memory. In Proceedings, Spring Compcon 1989, pages 184–190. IEEE Computer Society, San Francisco, CA., 1989.
D. L. Black and D. D. Sleator. Competitive algorithms for replication and migration problems. Technical Report CMU-CS-89-201, Department of Computer Science, Carnegie-Mellon University, 1989.
M. Chrobak, H. Karloff, T. Payne, and S. Vishwanathan. New results on server problems. SIAM Journal on Discrete Mathematics, 4: 172–181, 1991. Also in Proc. 1st ACM-SIAM Symp. on Discrete Algorithms, pages 291–300, 1990.
M. Chrobak and L. L. Larmore, Generosity helps, or an 11-competitive algorithm for three servers. In Proc. 3rd ACM-SIAM Symp. on Discrete Algorithms, pages 196–202, 1992.
M. Chrobak and L. L. Larmore, The server problem and on-line games, In Proceedings of the DIMACS Workshop on On-Line Algorithms, American Mathematical Society, vol. 7, pages 11–64, 1992.
W. Crowther, J. Goodhue, E. Starr, R. Thomas, W. Milliken, and T. Blackadar. Performance measurements on a 128-node butterfly parallel processor. In Proc. International Conf. on Parallel Processing, IEEE Computer Society, pages 531–540, 1985.
L. W. Dowdy and D. V. Foster. Comparative models of the file assignment problem. ACM Computing Surveys, 14(2):287–313, 1982.
Amos Fiat, Richard Karp, Michael Luby, Lyle McGeoch, Daniel D. Sleator, and Neil Young. On competitive algorithms for paging problems. Journal of Algorithms, 12(4):685–699, 1991.
A. Karlin, M. Manasse, L. Rudolph, and D. Sleator. Competitive snoopy caching. Algorithmica, 3(1):79–119, 1988.
A. R. Karlin, M. S. Manasse, L. A. McGeoch, and S. Owicki. Competitive randomized algorithms for non-uniform problems. In Proc. 1st ACM-SIAM Symp. on Discrete Algorithms, pages 301–309, 1990.
M. Manasse, L. A. McGeoch, and D. Sleator. Competitive algorithms for on-line problems. Journal of Algorithms, 11: 208–230, 1990. Also in Proc. 20th ACM Symposium on Theory of Computing, pages 322–333, 1988.
G. Pfister et. al. The IBM research parallel processor prototype: Introduction and architecture. In Proc. International Conf. on Parallel Processing, IEEE Computer Society, pages 764–771, 1985.
P. Raghavan and M. Snir. Memory versus randomization in on-line algorithms. Research Report RC 15622 (No. 69444), IBM T. J. Watson Research Center, 1990. Also in Proc. 16th International Colloquium on Automata, Languages, and Programming, Lecture Notes in Computer Science vol. 372, Springer-Verlag, pages 687–703, 1989.
C. Scheurich and M. Dubois. Dynamic page migration in multiprocessors with distributed global memory. IEEE Transactions on Computers, 38(8):1154–1163, August 1989.
J. Westbrook. Randomized algorithms for multiprocessor page migration. In Proceedings of the DIMACS Workshop on On-Line Algorithms, American Mathematical Society, vol. 7, pages 135–150, 1992.
A. Wilson. Hierarchical cache/bus architecture for shared memory multiprocessors. In Proc. 14th International Symp. on Computer Architecture, pages 244–252. ACM SIGARCH/IEEE Computer Society, 1987.
O. Wolfson. A distributed algorithm for adaptive replication data. Technical Report CUCS-057-90, Department of Computer Science, Columbia University, 1990.
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Chrobak, M., Larmore, L.L., Reingold, N., Westbrook, J. (1993). Page migration algorithms using work functions. In: Ng, K.W., Raghavan, P., Balasubramanian, N.V., Chin, F.Y.L. (eds) Algorithms and Computation. ISAAC 1993. Lecture Notes in Computer Science, vol 762. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57568-5_272
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DOI: https://doi.org/10.1007/3-540-57568-5_272
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