The zero-one principle for switching networks

ABSTRACT

Recently, approximation analysis has been extensively used to study algorithms for routing weighted packets in various network settings. Although different techniques were applied in the analysis of diverse models, one common property was evident: the analysis of input sequences composed solely of two different values is always substantially easier, and many results are known only for restricted value sequences. Motivated by this, we introduce our zero-one principle for switching networks which characterizes a wide range of algorithms for which achieving c-approximation (as well as c-competitiveness) with respect to sequences composed of 0's and 1's implies achieving c-approximation. The zero-one principle proves to be very efficient in the design of switching algorithms, and substantially facilitates their analysis. We present three applications. First, we consider the Multi-Queue QoS Switching model and design a 3-competitive algorithm, improving the result from [6]. Second, we study the Weighted Dynamic Routing problem on a line topology of length k and present a (k+1)-competitive algorithm, which improves and generalizes the results from [1,12]. As a third application, we consider the work of [11], that compares the performance of local algorithms to the global optimum in various network topologies, and generalize their results from 2-value sequences to arbitrary value sequences.

REFERENCES

• 1: William Aiello , Rafail Ostrovsky , Eyal Kushilevitz , Adi Rosén, Dynamic routing on networks with fixed-size buffers, Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms, January 12-14, 2003, Baltimore, Maryland
• 2: W. A. Aiello, Y. Mansour, S. Rajagopolan, and A. Rosen. Competitive queue policies for differentiated services. In Proceedings of the IEEE INFOCOM 2000, pages 431--440.
• 3: M. Ajtai , J. Komlós , E. Szemerédi, An 0(n log n) sorting network, Proceedings of the fifteenth annual ACM symposium on Theory of computing, p.1-9, December 1983 [doi>10.1145/800061.808726]
• 4: Nir Andelman , Yishay Mansour , An Zhu, Competitive queueing policies for QoS switches, Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms, January 12-14, 2003, Baltimore, Maryland
• 5: A. Fernandez, Universal stability results for greedy contention-resolution protocols, Proceedings of the 37th Annual Symposium on Foundations of Computer Science, p.380, October 14-16, 1996
• 6: Yossi Azar , Yossi Richter, Management of multi-queue switches in QoS networks, Proceedings of the thirty-fifth annual ACM symposium on Theory of computing, June 09-11, 2003, San Diego, CA, USA [doi>10.1145/780542.780556]
• 7: Alexander Birman , H. Richard Gail , Sidney L. Hantler , Zvi Rosberg , Moshe Sidi, An optimal service policy for buffer systems, Journal of the ACM (JACM), v.42 n.3, p.641-657, May 1995 [doi>10.1145/210346.210422]
• 8: Allan Borodin , Jon Kleinberg , Prabhakar Raghavan , Madhu Sudan , David P. Williamson, Adversarial queueing theory, Proceedings of the twenty-eighth annual ACM symposium on Theory of computing, p.376-385, May 22-24, 1996, Philadelphia, Pennsylvania, United States [doi>10.1145/237814.237984]
• 9: Thomas T. Cormen , Charles E. Leiserson , Ronald L. Rivest, Introduction to algorithms, MIT Press, Cambridge, MA, 1990
• 10: Ellen L. Hahne , Alexander Kesselman , Yishay Mansour, Competitve buffer management for shared-memory switches, Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures, p.53-58, July 2001, Crete Island, Greece [doi>10.1145/378580.378589]
• 11: A. Kesselman, Z. Lotker, Y. Mansour, and B. Patt-Shamir. Buffer overflows of merging streams. In Proc. 11th Annual European Symposium on Algorithms, pages 349--360, 2003.
• 12: Alexander Kesselman , Zvi Lotker , Yishay Mansour , Boaz Patt-Shamir , Baruch Schieber , Maxim Sviridenko, Buffer overflow management in QoS switches, Proceedings of the thirty-third annual ACM symposium on Theory of computing, p.520-529, July 2001, Hersonissos, Greece [doi>10.1145/380752.380847]
• 13: Alexander Kesselman , Yishay Mansour, Loss-bounded analysis for differentiated services, Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms, p.591-600, January 07-09, 2001, Washington, D.C., United States
• 14: Alex Kesselman , Adi Rosén, Scheduling policies for CIOQ switches, Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures, June 07-09, 2003, San Diego, California, USA [doi>10.1145/777412.777473]
• 15: Donald E. Knuth, The art of computer programming, volume 3: (2nd ed.) sorting and searching, Addison Wesley Longman Publishing Co., Inc., Redwood City, CA, 1998
• 16: Zvi Lotker , Boaz Patt-Shamir, Nearly optimal FIFO buffer management for DiffServ, Proceedings of the twenty-first annual symposium on Principles of distributed computing, July 21-24, 2002, Monterey, California [doi>10.1145/571825.571851]
• 17: M. May, J. C. Bolot, A. Jean-Marie, and C. Diot. Simple performance models of differentiated services for the internet. In Proceedings of the IEEE INFOCOM 1999, pages 1385--1394.

INDEX TERMS

Primary Classification:
  C. Computer Systems Organization
  C.2 COMPUTER-COMMUNICATION NETWORKS
      C.2.2 Network Protocols
          Subjects: Routing protocols

Additional Classification:
  F. Theory of Computation
  F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY
      F.2.2 Nonnumerical Algorithms and Problems

General Terms:
Algorithms, Theory

Keywords:
QoS, competitive, on-line, switch