Resource Allocation in Bounded Degree Trees

  • Reuven Bar-Yehuda
  • Michael Beder
  • Yuval Cohen
  • Dror Rawitz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4168)


We study the bandwidth allocation problem (bap) in bounded degree trees. In this problem we are given a tree and a set of connection requests. Each request consists of a path in the tree, a bandwidth requirement, and a weight. Our goal is to find a maximum weight subset S of requests such that, for every edge e, the total bandwidth of requests in S whose path contains e is at most 1. We also consider the storage allocation problem (sap), in which it is also required that every request in the solution is given the same contiguous portion of the resource in every edge in its path. We present a deterministic approximation algorithm for bap in bounded degree trees with ratio \((2\sqrt{e}-1)/(\sqrt{e}-1) \)+ ε< 3.542. Our algorithm is based on a novel application of the local ratio technique in which the available bandwidth is divided into narrow strips and requests with very small bandwidths are allocated in these strips. We also present a randomized (2+ε)-approximation algorithm for bap in bounded degree trees. The best previously known ratio for bap in general trees is 5. We present a reduction from sap to bap that works for instances where the tree is a line and the bandwidths are very small. It follows that there exists a (2+ε)-approximation algorithm for sap in the line. The best previously known ratio for this problem is 7.


Approximation Algorithm Connection Request Local Ratio Line Topology Degree Tree 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Golumbic, M.C.: Algorithmic Graph Theory and Perfect Graphs. Academic Press, London (1980)MATHGoogle Scholar
  2. 2.
    Tarjan, R.E.: Decomposition by clique separators. Discrete Mathematics 55, 221–232 (1985)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Arkin, E.M., Silverberg, E.B.: Scheduling jobs with fixed start and end times. Discrete Applied Mathematics 18, 1–8 (1987)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Bar-Noy, A., Canetti, R., Kutten, S., Mansour, Y., Schieber, B.: Bandwidth allocation with preemption. SIAM J. Comp. 28, 1806–1828 (1999)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Phillips, C., Uma, R.N., Wein, J.: Off-line admission control for general scheduling problems. Journal of Scheduling 3, 365–381 (2000)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Leonardi, S., Marchetti-Spaccamela, A., Vitaletti, A.: Approximation algorithms for bandwidth and storage allocation problems under real time constraints. In: Kapoor, S., Prasad, S. (eds.) FST TCS 2000. LNCS, vol. 1974, pp. 409–420. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  7. 7.
    Bar-Noy, A., Bar-Yehuda, R., Freund, A., Naor, J., Shieber, B.: A unified approach to approximating resource allocation and schedualing. J. ACM 48, 1069–1090 (2001)CrossRefMathSciNetGoogle Scholar
  8. 8.
    Chen, B., Hassin, R., Tzur, M.: Allocation of bandwidth and storage. IIE Transactions 34, 501–507 (2002)Google Scholar
  9. 9.
    Calinescu, G., Chakrabarti, A., Karloff, H.J., Rabani, Y.: Improved approximation algorithms for resource allocation. In: Cook, W.J., Schulz, A.S. (eds.) IPCO 2002. LNCS, vol. 2337, pp. 401–414. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  10. 10.
    Chakrabarti, A., Chekuri, C., Gupta, A., Kumar, A.: Approximation algorithms for the unsplittable flow problem. In: Jansen, K., Leonardi, S., Vazirani, V.V. (eds.) APPROX 2002. LNCS, vol. 2462, pp. 51–66. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  11. 11.
    Chekuri, C., Mydlarz, M., Shepherd, B.: Multicommodity demand flow in a tree. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 410–425. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  12. 12.
    Lewin-Eytan, L., Naor, J., Orda, A.: Admission control in networks with advance reservations. Algorithmica 40, 293–403 (2004)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Buchsbaum, A.L., Karloff, H., Kenyon, C., Reingold, N., Thorup, M.: OPT versus LOAD in dynamic storage allocation. SIAM J. Comp. 33, 632–646 (2004)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Bar-Yehuda, R., Even, S.: A local-ratio theorem for approximating the weighted vertex cover problem. Annals of Discrete Mathematics 25, 27–46 (1985)MathSciNetGoogle Scholar
  15. 15.
    Bafna, V., Berman, P., Fujito, T.: A 2-approximation algorithm for the undirected feedback vertex set problem. SIAM J. Disc. Math. 12, 289–297 (1999)MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Bar-Yehuda, R.: One for the price of two: A unified approach for approximating covering problems. Algorithmica 27, 131–144 (2000)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Reuven Bar-Yehuda
    • 1
  • Michael Beder
    • 1
  • Yuval Cohen
    • 1
  • Dror Rawitz
    • 2
  1. 1.Department of Computer ScienceTechnionHaifaIsrael
  2. 2.Caesarea Rothschild InstituteUniversity of HaifaHaifaIsrael

Personalised recommendations