Fast approximation of minimum multicast congestion - Implementation versus theory

Baltz, Andreas; Srivastav, Anand

doi:10.1051/ro:2004028

Baltz, Andreas ; Srivastav, Anand

RAIRO - Operations Research - Recherche Opérationnelle, Tome 38 (2004) no. 4, pp. 319-344.

Résumé

The problem of minimizing the maximum edge congestion in a multicast communication network generalizes the well-known $N P$ -hard multicommodity flow problem. We give the presently best theoretical approximation results as well as efficient implementations. In particular we show that for a network with $m$ edges and $k$ multicast requests, an $r (1 + ε) (r t e x t O P T + exp (1) ln m)$ -approximation can be computed in $O (k m ε^{- 2} ln k ln m)$ time, where $β$ bounds the time for computing an $r$ -approximate minimum Steiner tree. Moreover, we present a new fast heuristic that outperforms the primal-dual approaches with respect to both running time and objective value.

EuDML Zbl

DOI : 10.1051/ro:2004028

Classification : 68W25, 90C27
Mots-clés : combinatorial optimization, approximation algorithms

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     author = {Baltz, Andreas and Srivastav, Anand},
     title = {Fast approximation of minimum multicast congestion - {Implementation} versus theory},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {319--344},
     publisher = {EDP-Sciences},
     volume = {38},
     number = {4},
     year = {2004},
     doi = {10.1051/ro:2004028},
     zbl = {1114.90101},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/ro:2004028/}
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Baltz, Andreas; Srivastav, Anand. Fast approximation of minimum multicast congestion - Implementation versus theory. RAIRO - Operations Research - Recherche Opérationnelle, Tome 38 (2004) no. 4, pp. 319-344. doi : 10.1051/ro:2004028. https://www.numdam.org/articles/10.1051/ro:2004028/

Bibliographie
Cité par

[1] J. Aspnes, Y. Azar, A. Fiat, S. Plotkin and O. Waarts, On-line routing of virtual circuits with applications to load balancing and machine scheduling. J. Association Computing Machinery 44 (1997) 486-504. | Zbl

[2] R. Carr and S. Vempala, Randomized Metarounding, in Proc. of the 32nd ACM Symposium on the theory of computing (STOC '00), Portland, USA (2000) 58-62.

[3] N. Garg, J. Könemann, Faster and Simpler Algorithms for Multicommodity Flow and other Fractional Packing Problems, in Proc. 39th IEEE Annual Symposium on Foundations of Computer Science (1998) 300-309.

[4] A.V. Goldberg, A natural randomization strategy for multicommodity flow and related algorithms. Inform. Process. Lett. 42 (1992) 249-256. | Zbl

[5] A.V. Goldberg, A.D. Oldham, S. Plotkin and C. Stein, An Implementation of a Combinatorial Approximation Algorithm for Minimum-Cost Multicommodity Flows, in Proc. 6th Conf. on Integer Prog. and Combinatorial Optimization (1998) 338-352. | Zbl

[6] M.D. Grigoriadis and L.G. Khachiyan, Fast approximation schemes for convex programs with many blocks and coupling constraints. SIAM J. Optim. 4 (1994) 86-107. | Zbl

[7] K. Jansen and H. Zhang, An approximation algorithm for the multicast congestion problem via minimum Steiner trees, in Proc. 3rd Int. Worksh. on Approx. and Random. Alg. in Commun. Netw. (ARANCE'02), Roma, Italy, September 21. Carleton Scientific (2002) 77-90.

[8] K. Jansen and H. Zhang, Approximation algorithms for general packing problems with modified logarithmic potential function, in Proc. 2nd IFIP Int. Conf. on Theoretical Computer Science (TCS'02), Montréal, Québec, Canada, August 25-30 (2002).

[9] P. Klein, S. Plotkin, C. Stein and E. Tardos, Faster Approximation Algorithms for the Unit Capacity Concurrent Flow Problem with Applications to Routing and Finding Sparse Cuts. SIAM J. Comput. 23 (1994) 466-487. | Zbl

[10] T. Leighton, F. Makedon, S. Plotkin, C. Stein, E. Tardos and S. Tragoudas, Fast approximation algorithms for multicommodity flow problems. J. Comp. Syst. Sci. 50 (1995) 228-243. | Zbl

[11] D.W. Matula and F. Shahrokhi, The maximum concurrent flow problem. J. Association Computing Machinery 37 (1990) 318-334. | Zbl

[12] K. Mehlhorn, A faster approximation algorithm for the Steiner problem in graphs. Inform. Process. Lett. 27 (1998) 125-128. | Zbl

[13] S. Plotkin, D. Shmoys and E. Tardos, Fast approximation algorithms for fractional packing and covering problems. Math. Oper. Res. 20 (1995) 257-301. | Zbl

[14] T. Radzik, Fast deterministic approximation for the multicommodity flow problem. Math. Prog. 78 (1997) 43-58. | Zbl

[15] P. Raghavan, Probabilistic construction of deterministic algorithms: Approximating packing integer programs. J. Comp. Syst. Sci. 38 (1994) 683-707. | Zbl

[16] A. Srivastav and P. Stangier, On complexity, representation and approximation of integral multicommodity flows. Discrete Appl. Math. 99 (2000) 183-208. | Zbl

[17] S. Vempala and B. Vöcking, Approximating Multicast Congestion, in Proc. 10th ISAAC, Chennai, India (1999) 367-372. | Zbl

[18] G. Robins and A. Zelikovsky, Improved Steiner tree approximation in graphs, in Proc. of the 11th Annual ACM-SIAM Symp. on Discrete Algorithms (SODA 2000) (2000) 770-779. | Zbl

Correa, Oscar; Khan, A. K. M. Mustafizur Rahman; Tanin, Egemen; Kulik, Lars; Ramamohanarao, Kotagiri Congestion-Aware Ride-Sharing, ACM Transactions on Spatial Algorithms and Systems, Volume 5 (2019) no. 1, p. 1 | DOI:10.1145/3317639
Ghose, Rahul; Chattopadhyay, Soummyo Priyo; Das, Tiyasha; Das, Tejes; Saha, Ayoshna, 2015 International Conference and Workshop on Computing and Communication (IEMCON) (2015), p. 1 | DOI:10.1109/iemcon.2015.7344530
Baltz, Andreas; Srivastav, Anand Multicast Routing and Design of Sparse Connectors, Algorithmics of Large and Complex Networks, Volume 5515 (2009), p. 247 | DOI:10.1007/978-3-642-02094-0_12
Terlaky, Tamás; Vannelli, Anthony; Zhang, Hu On routing in VLSI design and communication networks, Discrete Applied Mathematics, Volume 156 (2008) no. 11, p. 2178 | DOI:10.1016/j.dam.2008.01.014
Saad, Mohamed; Terlaky, Tamás; Vannelli, Anthony; Zhang, Hu Packing trees in communication networks, Journal of Combinatorial Optimization, Volume 16 (2008) no. 4, p. 402 | DOI:10.1007/s10878-008-9150-4
Jansen, Klaus; Zhang, Hu Approximation algorithms for general packing problems and their application to the multicast congestion problem, Mathematical Programming, Volume 114 (2008) no. 1, p. 183 | DOI:10.1007/s10107-007-0106-8
Terlaky, Tamás; Vannelli, Anthony; Zhang, Hu On Routing in VLSI Design and Communication Networks, Algorithms and Computation, Volume 3827 (2005), p. 1051 | DOI:10.1007/11602613_104
Saad, Mohamed; Terlaky, Tamás; Vannelli, Anthony; Zhang, Hu Packing Trees in Communication Networks, Internet and Network Economics, Volume 3828 (2005), p. 688 | DOI:10.1007/11600930_69

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