Bayesian Generalized Network Design

Authors Yuval Emek, Shay Kutten, Ron Lavi, Yangguang Shi



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Yuval Emek
  • Faculty of Industrial Engineering and Management, Technion, Haifa, Israel
Shay Kutten
  • Faculty of Industrial Engineering and Management, Technion, Haifa, Israel
Ron Lavi
  • Faculty of Industrial Engineering and Management, Technion, Haifa, Israel
Yangguang Shi
  • Faculty of Industrial Engineering and Management, Technion, Haifa, Israel

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Yuval Emek, Shay Kutten, Ron Lavi, and Yangguang Shi. Bayesian Generalized Network Design. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 45:1-45:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.ESA.2019.45

Abstract

We study network coordination problems, as captured by the setting of generalized network design (Emek et al., STOC 2018), in the face of uncertainty resulting from partial information that the network users hold regarding the actions of their peers. This uncertainty is formalized using Alon et al.’s Bayesian ignorance framework (TCS 2012). While the approach of Alon et al. is purely combinatorial, the current paper takes into account computational considerations: Our main technical contribution is the development of (strongly) polynomial time algorithms for local decision making in the face of Bayesian uncertainty.

Subject Classification

ACM Subject Classification
  • Theory of computation → Approximation algorithms analysis
  • Theory of computation → Mathematical optimization
  • Theory of computation → Algorithm design techniques
Keywords
  • approximation algorithms
  • Bayesian competitive ratio
  • Bayesian ignorance
  • generalized network design
  • diseconomies of scale
  • energy consumption
  • smoothness
  • best response dynamics

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References

  1. Ajit Agrawal, Philip Klein, and R. Ravi. When Trees Collide: An Approximation Algorithm for the Generalized Steiner Problem on Networks. SIAM Journal on Computing, 24(3):440-456, 1995. Google Scholar
  2. Sebastian Aland, Dominic Dumrauf, Martin Gairing, Burkhard Monien, and Florian Schoppmann. Exact price of anarchy for polynomial congestion games. In Annual Symposium on Theoretical Aspects of Computer Science, pages 218-229. Springer, 2006. Google Scholar
  3. Susanne Albers. Energy-efficient Algorithms. Commun. ACM, 53(5):86-96, 2010. Google Scholar
  4. Noga Alon, Yuval Emek, Michal Feldman, and Moshe Tennenholtz. Bayesian ignorance. Theoretical Computer Science, 452:1-11, 2012. Preliminary version appears in Proceedings of the 29th ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, pp. 384-391. ACM, 2010. Google Scholar
  5. Matthew Andrews, Antonio Fernández Anta, Lisa Zhang, and Wenbo Zhao. Routing for Power Minimization in the Speed Scaling Model. IEEE/ACM Transactions on Networking, 20(1):285-294, February 2012. Google Scholar
  6. Evripidis Bampis, Alexander Kononov, Dimitrios Letsios, Giorgio Lucarelli, and Maxim Sviridenko. Energy efficient scheduling and routing via randomized rounding. In 33nd International Conference on Foundations of Software Technology and Theoretical Computer Science, page 449, 2013. Google Scholar
  7. Nikhil Bansal, Tracy Kimbrel, and Kirk Pruhs. Speed Scaling to Manage Energy and Temperature. J. ACM, 54(1):3:1-3:39, 2007. Google Scholar
  8. Daniel Berend and Tamir Tassa. Improved bounds on Bell numbers and on moments of sums of random variables. Probability and Mathematical Statistics, 30(2):185-205, 2010. Google Scholar
  9. Jarosław Byrka, Fabrizio Grandoni, Thomas Rothvoss, and Laura Sanità. Steiner tree approximation via iterative randomized rounding. Journal of the ACM (JACM), 60(1):6, 2013. Preliminary version in STOC'10. Google Scholar
  10. Moses Charikar, Chandra Chekuri, To-yat Cheung, Zuo Dai, Ashish Goel, Sudipto Guha, and Ming Li. Approximation Algorithms for Directed Steiner Problems. In Proceedings of the Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, pages 192-200, 1998. Google Scholar
  11. Chandra Chekuri, Guy Even, Anupam Gupta, and Danny Segev. Set Connectivity Problems in Undirected Graphs and the Directed Steiner Network Problem. ACM Trans. Algorithms, 7(2):18:1-18:17, 2011. Google Scholar
  12. Ken Christensen, Pedro Reviriego, Bruce Nordman, Michael Bennett, Mehrgan Mostowfi, and Juan Antonio Maestro. IEEE 802.3 az: the road to energy efficient ethernet. IEEE Communications Magazine, 48(11), 2010. Google Scholar
  13. Teodor Gabriel Crainic, Xiaorui Fu, Michel Gendreau, Walter Rei, and Stein W Wallace. Progressive hedging-based metaheuristics for stochastic network design. Networks, 58(2):114-124, 2011. Google Scholar
  14. E. W. Dijkstra. A Note on Two Problems in Connexion with Graphs. Numer. Math., 1(1):269-271, 1959. Google Scholar
  15. Yuval Emek, Shay Kutten, Ron Lavi, and Yangguang Shi. Approximating Generalized Network Design Under (Dis)Economies of Scale with Applications to Energy Efficiency. In Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2018, pages 598-606, New York, NY, USA, 2018. ACM. Google Scholar
  16. Yuval Emek, Shay Kutten, Ron Lavi, and Yangguang Shi. Bayesian Generalized Network Design. ArXiv e-prints, June 2019. URL: http://arxiv.org/abs/1907.00484.
  17. Matthias Englert and Harald Räcke. Oblivious Routing for the Lp-norm. In Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science, FOCS '09, pages 32-40, Washington, DC, USA, 2009. IEEE Computer Society. Google Scholar
  18. Matthias Englert and Harald Räcke. Oblivious routing for the Lp-norm. In Foundations of Computer Science, 2009. FOCS'09. 50th Annual IEEE Symposium on, pages 32-40. IEEE, 2009. Google Scholar
  19. Michael L. Fredman and Robert Endre Tarjan. Fibonacci Heaps and Their Uses in Improved Network Optimization Algorithms. J. ACM, 34(3):596-615, 1987. Google Scholar
  20. Naveen Garg, Anupam Gupta, Stefano Leonardi, and Piotr Sankowski. Stochastic analyses for online combinatorial optimization problems. In Proceedings of the Nineteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA '08, pages 942-951. Society for Industrial and Applied Mathematics, 2008. Google Scholar
  21. Anupam Gupta, Mohammad T Hajiaghayi, and Harald Räcke. Oblivious network design. In Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm, pages 970-979. Society for Industrial and Applied Mathematics, 2006. Google Scholar
  22. Anupam Gupta, R Ravi, and Amitabh Sinha. An edge in time saves nine: LP rounding approximation algorithms for stochastic network design. In FOCS, pages 218-227, 2004. Google Scholar
  23. Prahladh Harsha, Thomas P. Hayes, Hariharan Narayanan, Harald Räcke, and Jaikumar Radhakrishnan. Minimizing Average Latency in Oblivious Routing. In Proceedings of the Nineteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA '08, pages 200-207, Philadelphia, PA, USA, 2008. Society for Industrial and Applied Mathematics. Google Scholar
  24. Intel. Enhanced Intel Speedstep Technology for the Intel Pentium M Processor. In Intel White Paper 301170-001, 2004. Google Scholar
  25. Sandy Irani and Kirk R. Pruhs. Algorithmic Problems in Power Management. SIGACT News, 36(2):63-76, 2005. Google Scholar
  26. J.L.W.V. Jensen. Sur les fonctions convexes et les inégalités entre les valeurs moyennes. Acta Mathematica, 30(1):175-193, 1906. Google Scholar
  27. Gregory Lawler and Hariharan Narayanan. Mixing Times and &Ell;P Bounds for Oblivious Routing. In Proceedings of the Meeting on Analytic Algorithmics and Combinatorics, ANALCO '09, pages 66-74, Philadelphia, PA, USA, 2009. Society for Industrial and Applied Mathematics. Google Scholar
  28. Konstantin Makarychev and Maxim Sviridenko. Solving Optimization Problems with Diseconomies of Scale via Decoupling. In 55th IEEE Annual Symposium on Foundations of Computer Science, FOCS, 2014. Google Scholar
  29. Sergiu Nedevschi, Lucian Popa, Gianluca Iannaccone, Sylvia Ratnasamy, and David Wetherall. Reducing Network Energy Consumption via Sleeping and Rate-adaptation. In Proceedings of the 5th USENIX Symposium on Networked Systems Design and Implementation, NSDI'08, pages 323-336. USENIX Association, 2008. Google Scholar
  30. Harald Räcke. Survey on Oblivious Routing Strategies. In Mathematical Theory and Computational Practice, volume 5635 of Lecture Notes in Computer Science, pages 419-429. Springer Berlin Heidelberg, 2009. Google Scholar
  31. Ragheb Rahmaniani, Teodor Gabriel Crainic, Michel Gendreau, and Walter Rei. Accelerating the Benders Decomposition Method: Application to Stochastic Network Design Problems. SIAM Journal on Optimization, 28(1):875-903, 2018. Google Scholar
  32. Tim Roughgarden. The price of anarchy in games of incomplete information. In Proceedings of the 13th ACM Conference on Electronic Commerce, pages 862-879. ACM, 2012. Google Scholar
  33. Tim Roughgarden. Intrinsic robustness of the price of anarchy. Journal of the ACM (JACM), 62(5):32, 2015. Preliminary version in STOC'09. Google Scholar
  34. I Richard Savage. Probability inequalities of the Tchebycheff type. Journal of Research of the National Bureau of Standards-B. Mathematics and Mathematical Physics B, 65(3):211-222, 1961. Google Scholar
  35. Yangguang Shi, Fa Zhang, Jie Wu, and Zhiyong Liu. Randomized oblivious integral routing for minimizing power cost. Theoretical Computer Science, 607:221-246, 2015. Google Scholar
  36. Adam Wierman, Lachlan LH Andrew, and Ao Tang. Power-Aware Speed Scaling in Processor Sharing Systems. In 28th IEEE International Conference on Computer Communications, Joint Conference of the IEEE Computer and Communications Societies, INFOCOM, pages 2007-2015, April 2009. Google Scholar
  37. F. Yao, A. Demers, and S. Shenker. A scheduling model for reduced CPU energy. In Proceedings of IEEE 36th Annual Foundations of Computer Science, pages 374-382, 1995. Google Scholar
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