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Design and Analysis of Dynamic Processes: A Stochastic Approach (Invited Paper)

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Algorithms — ESA’ 98 (ESA 1998)

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Abstract

Past research in theoretical computer science has focused mainly on static computation problems, where the input is known before the start of the computation and the goal is to minimize the number of steps till termination with a correct output. Many important processes in today’s computing are dynamic processes, whereby input is continuously injected to the system, and the algorithm is measured by its long term, steady state, performance. Examples of dynamic processes include communication protocols, memory management tools, and time sharing policies. Our goal is to develop new tools for the design and analyzing the performance of dynamic processes, in particular through modeling the dynamic process as an infinite stochastic processes.

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References

  1. D. Aldous. Ultimate instability of exponential back-off protocol for acknowledgment based transmission control of random access communication channels. IEEE Transactions on Information Theory, Vol. IT-33, 1987, pp. 219–223.

    Article  MathSciNet  Google Scholar 

  2. M. Andrew, B. Awerbuch, A Fernandez, J. Kleinberg, T. Leighton, and Z. Liu. Universal stability results for greedy contention-resolution protocols. Proceedings of the 37th Annual Synp. on Foundations of Computer Science, pages 380–389, 1997.

    Google Scholar 

  3. B. Awerbuch, Y. Azar, and S. Plotkin. Throughput competitive online routing. In Proceedings of the 34th IEEE Conference on Foundations of Computer Science, pages 32–40, 1993.

    Google Scholar 

  4. B. Awerbuch, R. Gawlick, T. Leighton, and Y. Rabani. On-line admission control and circuit routing for high-performance computing and communication. Proceedings of the 35th Annual Synp. on Foundations of Computer Science, October 1994, pp 412–423.

    Google Scholar 

  5. Y. Azar, A. Z. Broder, A. R. Karlin, and E. Upfal. Balanced allocations. In Proceedings of the 26th Annual ACM Symposium on Theory of Computing, pages 593–602, 1994.

    Google Scholar 

  6. Y. Azar, J. Naor, and R. Rom. The competitiveness of on-line assignments. In Proceedings of the 3rd Annual ACM-SIAM Symposium on Discrete Algorithms, pages 203–210, 1992.

    Google Scholar 

  7. A. Borodin, J. Kleinberg, P. Raghavan, M. Sudan and D. P. Williamson Adversarial queuing theory. Proceedings of the 28th Annual ACM Symposium on Theory of Computing, pp. 376–385, 1996.

    Google Scholar 

  8. A. Z. Broder and E. Upfal. Dynamic Deflection Routing in Arrays. Proceedings of the 28th Annual ACM Symposium on Theory of Computing, pp. 348–355, 1996.

    Google Scholar 

  9. A. Z. Broder, A.M. Frieze, and E. Upfal. “A general approach to dynamic packet routing with bounded buffers.” Proceedings of the 37th IEEE Symp. on Foundations of Computer Science. Burlington, 1996, pp. 390–399.

    Google Scholar 

  10. A. Z. Broder, A.M. Frieze, and E. Upfal. “Static and dynamic path selection on expander graphs: a random walk approach”. Proceedings of the 29th ACM Symp. on Theory of Computing. El Paso, 1997.

    Google Scholar 

  11. A. Broder, A. Frieze, and E. Upfal. “Dynamic packet routing on arrays with bounded buffers”. Third Latin American Symposium on Theoretical Informatics-LATIN’ 98 Campinas, Brazil. April 1998. In Springer-Verlag Lecture Notes in Computer Science 1380, pp 273–281, 1998.

    Article  MathSciNet  Google Scholar 

  12. R. L. Cruz. A calculus for network delay, part I: Network elements in isolation. IEEE Trans. on Information Theory, Vol. 37, pages 114–131, 1991

    Article  MATH  MathSciNet  Google Scholar 

  13. R. L. Cruz. A calculus for network delay, part II: Network analysis in isolation. IEEE Trans. on Information Theory, Vol. 37, pages 132–141, 1991

    Article  MATH  MathSciNet  Google Scholar 

  14. A. Czumaj and V. Stemann. “Randomized Allocation Processes”. Preprint, 1997.

    Google Scholar 

  15. M. Dietzfelbinger, A. R. Karlin, K. Mehlhorn, F. Meyer auf der Heide, H. Rohnert, and R. E. Tarjan. Dynamic perfect hashing: Upper and lower bounds. In Proceedings of the 29th IEEE Conference on Foundations of Computer Science, pages 524–531, 1988.

    Google Scholar 

  16. L. A. Goldberg and P.D. MacKenzie. Contention Resolution with Guaranteed Constant Expected Delay. Preprint, 1997.

    Google Scholar 

  17. J. Goodman, A.G. Greenberg, N. Madras, and P. March. Stability of Binary Exponential Backoff. J. of the ACM, Vol. 35 (1988) pages 579–602.

    Article  MathSciNet  Google Scholar 

  18. A. G. Greenberg, P. Flajolet, and R.E. Ladner. Estimating the Multiplicities of Conflicts to Speed Their Resolution in Multiple Access Channels. J. of the ACM, Vol. 34, 1987, pp. 289–325.

    Article  MATH  MathSciNet  Google Scholar 

  19. J. Håstad, T. Leighton, and B. Rogoff. Analysis of backoff protocols for multiple access channels. Proceedings of the 19th ACM Symp. on Theory of Computing, 1987, pp. 241–253.

    Google Scholar 

  20. M. Harcol-Balter and P. Black. Queuing analysis of oblivious packet routing networks. Procs. of the 5th Annual ACM-SIAM Symp. on Discrete Algorithms. Pages 583–592, 1994.

    Google Scholar 

  21. M. Harcol-Balter and D. Wolf. Bounding delays in packet-routing networks. Procs. of the 27th Annual ACM Symp. on Theory of Computing, 1995, pp. 248–257.

    Google Scholar 

  22. R. M. Karp, M. Luby, and F. Meyer auf der Heide. Efficient PRAM simulation on a distributed memory machine. In Proceedings of the 24th Annual ACM Symposium on Theory of Computing, pages 318–326, 1992.

    Google Scholar 

  23. A. Kamath, O. Palmon, and S. Plotkin. Routing and Admission Control in General Topology Networks with Poisson Arrivals. SODA 96.

    Google Scholar 

  24. F. P. Kelley. Blocking probabilities in large circuit-switching networks. Adv. Appl. Prob., 18:573–505, 1986.

    Google Scholar 

  25. F. P. Kelly. Stochastic models of computer communication systems. J. Royal Statistical Soc. B, Vol. 47, 1985, pp. 379–395.

    MATH  Google Scholar 

  26. L. Kleinrock. Queueing systems. Wiley, New York, 1975.

    MATH  Google Scholar 

  27. N. Kahale and T. Leighton. Greedy dynamic routing on arrays. Procs. of the 6th Annual ACM-SIAM Symp. on Discrete Algorithms. Pages 558–566, 1995.

    Google Scholar 

  28. T. Leighton. Average case analysis of greedy routing algorithms on arrays. Procs. of the Second Annual ACM Symp. on Parallel Algorithms and Architectures. Pages 2–10, 1990.

    Google Scholar 

  29. F. T. Leighton. Introduction to Parallel Algorithms and Architectures. Morgan-Kaufmann, San Mateo, CA 1992.

    MATH  Google Scholar 

  30. F. T. Leighton and S. Rao. Circuit switching: a multi-commodity flow based approach. Proc. of 9th International Parallel Processing Symposium, 1995.

    Google Scholar 

  31. P. D. MacKenzie, C.G. Plaxton, and R. Rajaraman. On contention resolution protocols and associated probabilistic phenomena. Proceedings of the 26th ACM Symposium on Theory of Computing, 1994, pp. 153–162.

    Google Scholar 

  32. R. Metcalfe and D. Boggs. Ethernet: distributed packet switching for local computer networks. Communication of the ACM, Vol. 19, 1976, pp. 395–404.

    Article  Google Scholar 

  33. M. Mitzenmacher. Bounds on the greedy algorithms for array networks. Procs. of the 6th Annual ACM Symp. on Parallel Algorithms and Architectures. Pages 346–353, 1994.

    Google Scholar 

  34. M. Mitzenmacher. Load balancing and density dependent jump Markov processes. Procs. of the 37th IEEE Annual Symp. on Foundations of Computer Science, pages 213–222, October 1996.

    Google Scholar 

  35. M. Paterson and A. Srinivasan. Contention resolution with bounded delay. Proc. of the 34th Annual IEEE Symp. on Foundation of Computer Science, pages 104–113, 1995.

    Google Scholar 

  36. P. Raghavan and E. Upfal. St9chastic contention resolution with short delays. Proc. of 24th ACM Symp. on Theory of Computing, pages 229–237, 1995.

    Google Scholar 

  37. C. Scheideler and B. Voecking Universal continuous routing strategies. Procs. of the 8th Annual ACM Symp. on Parallel Algorithms and Architectures. 1996.

    Google Scholar 

  38. G. D. Stamoulis and J. N. Tsitsiklis. The effciency of greedy routing in hypercubes and butterflies. Procs. of the 6th Annual ACM Symp. on Parallel Algorithms and Architectures. Pages 346–353, 1994.

    Google Scholar 

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© 1998 Springer-Verlag Berlin Heidelberg

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Upfal, E. (1998). Design and Analysis of Dynamic Processes: A Stochastic Approach (Invited Paper). In: Bilardi, G., Italiano, G.F., Pietracaprina, A., Pucci, G. (eds) Algorithms — ESA’ 98. ESA 1998. Lecture Notes in Computer Science, vol 1461. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-68530-8_2

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  • DOI: https://doi.org/10.1007/3-540-68530-8_2

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