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Network Resilience and the Length-Bounded Multicut Problem: Reaching the Dynamic Billion-Scale with Guarantees

Published:03 April 2018Publication History
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Abstract

Motivated by networked systems in which the functionality of the network depends on vertices in the network being within a bounded distance T of each other, we study the length-bounded multicut problem: given a set of pairs, find a minimum-size set of edges whose removal ensures the distance between each pair exceeds T. We introduce the first algorithms for this problem capable of scaling to massive networks with billions of edges and nodes: three highly scalable algorithms with worst-case performance ratios. Furthermore, one of our algorithms is fully dynamic, capable of updating its solution upon incremental vertex / edge additions or removals from the network while maintaining its performance ratio. Finally, we show that unless NPBPP, there is no polynomial-time, approximation algorithm with performance ratio better than $Ømega (T)$, which matches the ratio of our dynamic algorithm up to a constant factor.

References

  1. Vijay V. Vazirani. Approximation Algorithms. Springer-Verlag Berlin Heidelberg, first edition, 2003.Google ScholarGoogle Scholar
  2. Tony H. Grubesic, Timothy C. Matisziw, Alan T. Murray, and Diane Snediker. Comparative Approaches for Assessing Network Vulnerability. International Regional Science Review, 31(1):88--112, 2008.Google ScholarGoogle ScholarCross RefCross Ref
  3. Arunabha Sen, Sudheendra Murthy, and Sujogya Banerjee. Region-based connectivity - A new paradigm for design of fault-tolerant networks. In 2009 International Conference on High Performance Switching and Routing, HPSR 2009, 2009. Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. Li Da Xu, Wu He, and Shancang Li. Internet of things in industries: A survey. IEEE Transactions on Industrial Informatics, 10(4):2233--2243, 2014.Google ScholarGoogle Scholar
  5. Linus Thrybom and Gunnar Prytz. QoS in Switched Industrial Ethernet. IEEE Conference on Emerging Technologies and Factory Automation, 2009. Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. Amazon.com. Amazon.com Help: Guaranteed Delivery Terms and Conditions. https://www.amazon.com/gp/help/customer/display.html?ie=UTF8&nodeId=201910260. Accessed: 2017-10-01.Google ScholarGoogle Scholar
  7. A. Kuhnle, T. Pan, V.G. Crawford, M.A. Alim, and M.T. Thai. Pseudo-separation for assessment of structural vulnerability of a network. In SIGMETRICS 2017 Abstracts - Proceedings of the 2017 ACM SIGMETRICS / International Conference on Measurement and Modeling of Computer Systems, 2017. Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. Jure Leskovec and Andrej Krevl. SNAP Datasets: Stanford Large Network Dataset Collection. http://snap.stanford.edu/ data. Accessed: 2017--10-01.Google ScholarGoogle Scholar
  9. Jure Leskovec, Jon Kleinberg, and Christos Faloutsos. Graphs over Time: Densification Laws, Shrinking Diameters and Possible Explanations. In ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD), pages 177--187, 2005. Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. Chunsheng Zhu, Lei Shu, Takahiro Hara, Lei Wang, Shojiro Nishio, and Laurence T. Yang. A survey on communication and data management issues in mobile sensor networks. Wireless Communications and Mobile Computing, 14:19--36, 2014.Google ScholarGoogle ScholarCross RefCross Ref
  11. Qingchen Zhang, Chunsheng Zhu, Laurence T Yang, Zhikui Chen, Liang Zhao, and Peng Li. An Incremental CFS Algorithm for Clustering Large Data in Industrial Internet of Things. IEEE Transactions on Industrial Informatics, 13(3):1193--1201, 2017.Google ScholarGoogle ScholarCross RefCross Ref
  12. Euiwoong Lee. Improved Hardness for Cut, Interdiction, and Firefighter Problems. Arxiv preprint arxiv:1607.05133v1, 2016.Google ScholarGoogle Scholar
  13. Michael Sipser. Introduction to the Theory of Computation. Thomson Course Technology, second edition, 2006.Google ScholarGoogle Scholar
  14. Alan Kuhnle. Source code link. https://gitlab.com/kuhnle/multi-pcut.Google ScholarGoogle Scholar
  15. Georg Baier, Thomas Erlebach, Alexander Hall, Ekkehard Koehler, Petr Kolman, Ondrej Pangrac, Heiko Schilling, and Martin Skutella. Length-Bounded Cuts and Flows. ACM Transactions on Algorithms, 7(1):1--27, 2010. Google ScholarGoogle ScholarDigital LibraryDigital Library
  16. Petr A. Golovach and Dimitrios M. Thilikos. Paths of bounded length and their cuts: Parameterized complexity and algorithms. Discrete Optimization, 8(1):72--86, 2011. Google ScholarGoogle ScholarDigital LibraryDigital Library
  17. Pavel Dvorak and Dusan Knop. Parameterized Complexity of Length-Bounded Cuts and Multi-cuts. In Theory and Applications of Models of Computation: 12th Annual Conference, pages 441?-452. Springer International Publishing, 2015.Google ScholarGoogle Scholar
  18. Dániel Marx. Parameterized complexity and approximation algorithms. The Computer Journal, 51(1):60--78, 2008. Google ScholarGoogle ScholarDigital LibraryDigital Library
  19. K. Malik, A. K. Mittal, and S. K. Gupta. The k most vital arcs in the shortest path problem. Operations Research Letters, 8(4):223--227, 1989. Google ScholarGoogle ScholarDigital LibraryDigital Library
  20. Eitan Israeli and R. Kevin Wood. Shortest-Path Network Interdiction. Networks, 40(2):97--111, 2002.Google ScholarGoogle Scholar
  21. Gerald Brown, Matthew Carlyle, Javier Salmerón, and Kevin Wood. Defending critical infrastructure. Interfaces, 36(6):530--544, 2006.Google ScholarGoogle ScholarCross RefCross Ref
  22. Justin Yates and Irene Casas. Role of Spatial Data in the Protection of Critical Infrastructure and Homeland Defense. Applied Spatial Analysis and Policy, 5(1):1--23, 2012.Google ScholarGoogle ScholarCross RefCross Ref
  23. Naveen Garg, Vijay V. Vaziranit, and Mihalis Yannakakis. Approximate max-flow min-(multi)cut theorems and their applications. In Proceedings of the twenty-fifth annual ACM Symposium on Theory of Computing., pages 698--707, 1993. Google ScholarGoogle ScholarDigital LibraryDigital Library
  24. A. Gupta. Improved results for directed multicut. In Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pages 454--455, 2003. Google ScholarGoogle ScholarDigital LibraryDigital Library
  25. Amit Agarwal, Noga Alon, and Moses S. Charikar. Improved approximation for directed cut problems. In Proceedings of the thirty-ninth annual ACM symposium on Theory of Computing, pages 671--680, New York, NY USA, 2007. ACM. Google ScholarGoogle ScholarDigital LibraryDigital Library
  26. Ben Roberts and Dirk P. Kroese. Estimating the Number of s-t Paths in a Graph. Journal of Graph Algorithms and Applications, 11(1):195--214, 2007.Google ScholarGoogle ScholarCross RefCross Ref
  27. Peng Jun Wan, Ding Zhu Du, Panos Pardalos, and Weili Wu. Greedy approximations for minimum submodular cover with submodular cost. Computational Optimization and Applications, 45(2):463--474, 2010. Google ScholarGoogle ScholarDigital LibraryDigital Library
  28. T. Soma and Y. Yoshida. A Generalization of Submodular Cover via the Diminishing Return Property on the Integer Lattice. Advances in Neural Information Processing ..., pages 1--9, 2015. Google ScholarGoogle ScholarDigital LibraryDigital Library
  29. Luigi Atzori, Antonio Iera, and Giacomo Morabito. The Internet of Things: A survey. Computer Networks, 54(15):2787--2805, 2010. Google ScholarGoogle ScholarDigital LibraryDigital Library
  30. Ahmad-Reza Sadeghi, Christian Wachsmann, and Michael Waidner. Security and Privacy Challenges in Industrial Internet of Things. Proceedings of the 52nd Annual Design Automation Conference on - DAC '15, 17:1--6, 2015. {31} Inc. Institute of Electrical and Electronics Engineers. IEEE 802.1 Time-Sensitive Networking Task Group. Google ScholarGoogle ScholarDigital LibraryDigital Library
  31. Kaixin Xu Kaixin Xu, Xiaoyan Hong Xiaoyan Hong, Mario Gerla Mario Gerla, Henry Ly, D.L. Daniel Lihui Gu, and Los Angeles. Landmark routing in large wireless battlefield networks using UAVs. 2001 MILCOM Proceedings Communications for Network-Centric Operations: Creating the Information Force (Cat. No.01CH37277), 1(c):230--234, 2001.Google ScholarGoogle ScholarCross RefCross Ref
  32. Syed R. Ali and Richard S. Wexler. Army Warfighter Information Network-Tactical ( Win-T ) Theory of Operation. In IEEE Military Communications Conference (MILCOM). IEEE, 2013.Google ScholarGoogle Scholar
  33. Juan C. Juarez, Anurag Dwivedi, a. Roger Hammons, Steven D. Jones, Vijitha Weerackody, and Robert a. Nichols. Free-space optical communications for next-generation military networks. IEEE Communications Magazine, 44(November):46--51, 2006. Google ScholarGoogle ScholarDigital LibraryDigital Library
  34. Venkatesan Guruswami and Euiwoong Lee. Inapproximability of Feedback Vertex Set for Bounded Length Cycles. In Electronic Colloquium on Computation Complexity (ECCC), volume 21, page 2, 2014.Google ScholarGoogle Scholar
  35. Wassily Hoeffding. Probability Inequalities for Sums of Bounded Random Variables. Journal of the American Statistical Association, 58(301):13--30, 1963.Google ScholarGoogle ScholarCross RefCross Ref
  36. Peter E. Hart, Nils J. Nilsson, and Bertram Raphael. Formal Basis for the Heuristic Determination of Minimum Cost Paths. Systems Science and Cybernetics, 4(2):100--107, 1968.Google ScholarGoogle ScholarCross RefCross Ref
  37. Guoliang Xue, Arunabha Sen, Weiyi Zhang, Jian Tang, and Krishnaiya Thulasiraman. Finding a path subject to many additive QoS constraints. IEEE/ACM Transactions on Networking, 15(1):201--211, 2007. Google ScholarGoogle ScholarDigital LibraryDigital Library
  38. Ying Xuan, Yilin Shen, Nam P. Nguyen, and My T. Thai. A graph-theoretic QoS-aware vulnerability assessment for network topologies. GLOBECOM - IEEE Global Telecommunications Conference, 2010.Google ScholarGoogle ScholarCross RefCross Ref
  39. Thomas Brinkhoff. Generating Network-Based Moving Objects. In IEEE 12th International Conference on Scientific and Statistical Database Management, pages 8--10, 2000. Google ScholarGoogle ScholarDigital LibraryDigital Library

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