Document Open Access Logo

Routing Symmetric Demands in Directed Minor-Free Graphs with Constant Congestion

Authors Timothy Carpenter, Ario Salmasi, Anastasios Sidiropoulos



PDF
Thumbnail PDF

File

LIPIcs.APPROX-RANDOM.2019.14.pdf
  • Filesize: 0.55 MB
  • 15 pages

Document Identifiers

Author Details

Timothy Carpenter
  • Dept. of Computer Science & Engineering, The Ohio State University, Columbus, OH, USA
Ario Salmasi
  • Dept. of Computer Science & Engineering, The Ohio State University, Columbus, OH, USA
Anastasios Sidiropoulos
  • Dept. of Computer Science, University of Illinois at Chicago, USA

Cite AsGet BibTex

Timothy Carpenter, Ario Salmasi, and Anastasios Sidiropoulos. Routing Symmetric Demands in Directed Minor-Free Graphs with Constant Congestion. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 145, pp. 14:1-14:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2019.14

Abstract

The problem of routing in graphs using node-disjoint paths has received a lot of attention and a polylogarithmic approximation algorithm with constant congestion is known for undirected graphs [Chuzhoy and Li 2016] and [Chekuri and Ene 2013]. However, the problem is hard to approximate within polynomial factors on directed graphs, for any constant congestion [Chuzhoy, Kim and Li 2016]. Recently, [Chekuri, Ene and Pilipczuk 2016] have obtained a polylogarithmic approximation with constant congestion on directed planar graphs, for the special case of symmetric demands. We extend their result by obtaining a polylogarithmic approximation with constant congestion on arbitrary directed minor-free graphs, for the case of symmetric demands.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
Keywords
  • Routing
  • Node-disjoint
  • Symmetric demands
  • Minor-free graphs

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads

References

  1. Alok Aggarwal, Amotz Bar-Noy, Don Coppersmith, Rajiv Ramaswami, Baruch Schieber, and Madhu Sudan. Efficient Routing and Scheduling Algorithms for Optical Networks. In Proceedings of the Fifth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA '94, pages 412-423, Philadelphia, PA, USA, 1994. Society for Industrial and Applied Mathematics. Google Scholar
  2. B. Awerbuch, R. Gawlick, T. Leighton, and Y. Rabani. On-line Admission Control and Circuit Routing for High Performance Computing and Communication. In Proceedings of the 35th Annual Symposium on Foundations of Computer Science, FOCS '94, pages 412-423, Washington, DC, USA, 1994. IEEE Computer Society. Google Scholar
  3. Andrei Z. Broder, Alan M. Frieze, and Eli Upfal. Existence and Construction of Edge-Disjoint Paths on Expander Graphs. SIAM Journal on Computing, 23(5):976-989, 1994. Google Scholar
  4. Chandra Chekuri and Alina Ene. Poly-logarithmic Approximation for Maximum Node Disjoint Paths with Constant Congestion. In Proceedings of the Twenty-fourth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA '13, pages 326-341, Philadelphia, PA, USA, 2013. Society for Industrial and Applied Mathematics. Google Scholar
  5. Chandra Chekuri and Alina Ene. The all-or-nothing flow problem in directed graphs with symmetric demand pairs. Mathematical Programming, 154(1):249-272, December 2015. Google Scholar
  6. Chandra Chekuri, Alina Ene, and Marcin Pilipczuk. Constant Congestion Routing of Symmetric Demands in Planar Directed Graphs. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016), Leibniz International Proceedings in Informatics (LIPIcs), pages 7:1-7:14, 2016. Google Scholar
  7. Chandra Chekuri, Sanjeev Khanna, and F. Bruce Shepherd. The All-or-nothing Multicommodity Flow Problem. In Proceedings of the Thirty-sixth Annual ACM Symposium on Theory of Computing, STOC '04, pages 156-165, New York, NY, USA, 2004. ACM. Google Scholar
  8. Chandra Chekuri, Sanjeev Khanna, and F. Bruce Shepherd. Multicommodity Flow, Well-linked Terminals, and Routing Problems. In Proceedings of the Thirty-seventh Annual ACM Symposium on Theory of Computing, STOC '05, pages 183-192, New York, NY, USA, 2005. ACM. Google Scholar
  9. Chandra Chekuri, Sanjeev Khanna, and F. Bruce Shepherd. An O(√n) approximation and integrality gap for disjoint paths and unsplittable flow. Theory of Computing, 2:2006, 2006. Google Scholar
  10. Chandra Chekuri and Anastasios Sidiropoulos. Approximation algorithms for Euler genus and related problems. In Foundations of Computer Science (FOCS), 2013 IEEE 54th Annual Symposium on, pages 167-176. IEEE, 2013. Google Scholar
  11. Julia Chuzhoy, Venkatesan Guruswami, Sanjeev Khanna, and Kunal Talwar. Hardness of Routing with Congestion in Directed Graphs. In Proceedings of the Thirty-ninth Annual ACM Symposium on Theory of Computing, STOC '07, pages 165-178, New York, NY, USA, 2007. ACM. Google Scholar
  12. Julia Chuzhoy and David H. K. Kim. On Approximating Node-Disjoint Paths in Grids. In Naveen Garg, Klaus Jansen, Anup Rao, and José D. P. Rolim, editors, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015), volume 40 of Leibniz International Proceedings in Informatics (LIPIcs), pages 187-211, Dagstuhl, Germany, 2015. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik. Google Scholar
  13. Julia Chuzhoy, David HK Kim, and Shi Li. Improved approximation for node-disjoint paths in planar graphs. In Proceedings of the forty-eighth annual ACM symposium on Theory of Computing, pages 556-569. ACM, 2016. Google Scholar
  14. Julia Chuzhoy, David HK Kim, and Rachit Nimavat. New hardness results for routing on disjoint paths. In Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing, pages 86-99. ACM, 2017. Google Scholar
  15. Julia Chuzhoy and Shi Li. A polylogarithmic approximation algorithm for edge-disjoint paths with congestion 2. In 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science, pages 233-242. IEEE, 2012. Google Scholar
  16. Erik D Demaine, Mohammad Taghi Hajiaghayi, and Ken-ichi Kawarabayashi. Algorithmic graph minor theory: Decomposition, approximation, and coloring. In Foundations of Computer Science, 2005. FOCS 2005. 46th Annual IEEE Symposium on, pages 637-646. IEEE, 2005. Google Scholar
  17. Erik D Demaine and MohammadTaghi Hajiaghayi. Linearity of grid minors in treewidth with applications through bidimensionality. Combinatorica, 28(1):19-36, 2008. Google Scholar
  18. Erik D Demaine, MohammadTaghi Hajiaghayi, Naomi Nishimura, Prabhakar Ragde, and Dimitrios M Thilikos. Approximation algorithms for classes of graphs excluding single-crossing graphs as minors. Journal of Computer and System Sciences, 69(2):166-195, 2004. Google Scholar
  19. Thor Johnson, Neil Robertson, P.D. Seymour, and Robin Thomas. Directed Tree-Width. Journal of Combinatorial Theory, Series B, 82(1):138-154, 2001. Google Scholar
  20. R M Karp. On the complexity of combinatorial problems. Networks, 5:45-68, 1975. Google Scholar
  21. Ken-ichi Kawarabayashi and Anastasios Sidiropoulos. Polylogarithmic approximation for minimum planarization (almost). In Foundations of Computer Science (FOCS), 2017 IEEE 58th Annual Symposium on, pages 779-788. IEEE, 2017. Google Scholar
  22. Stavros G Kolliopoulos and Clifford Stein. Approximating disjoint-path problems using greedy algorithms and packing integer programs. In International Conference on Integer Programming and Combinatorial Optimization, pages 153-168. Springer, 1998. Google Scholar
  23. D. Peleg and E. Upfal. Constructing disjoint paths on expander graphs. Combinatorica, 9(3):289-313, September 1989. Google Scholar
  24. Prabhakar Raghavan and Eli Upfal. Efficient Routing in All-optical Networks. In Proceedings of the Twenty-sixth Annual ACM Symposium on Theory of Computing, STOC '94, pages 134-143, New York, NY, USA, 1994. ACM. Google Scholar
  25. B. Reed. Introducing Directed Tree Width. Electronic Notes in Discrete Mathematics, 3(Supplement C):222-229, 1999. 6th Twente Workshop on Graphs and Combinatorial Optimization. Google Scholar
  26. N. Robertson and P.D. Seymour. Graph Minors. XIII. The Disjoint Paths Problem. Journal of Combinatorial Theory, Series B, 63(1):65-110, 1995. Google Scholar
  27. Neil Robertson and Paul D Seymour. Graph minors. XVI. Excluding a non-planar graph. Journal of Combinatorial Theory, Series B, 89(1):43-76, 2003. Google Scholar
  28. Carsten Thomassen. A simpler proof of the excluded minor theorem for higher surfaces. Journal of Combinatorial Theory, Series B, 70(2):306-311, 1997. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail