# Fast approximation of minimum multicast congestion – Implementation VERSUS Theory

Andreas Baltz; Anand Srivastav

RAIRO - Operations Research (2010)

- Volume: 38, Issue: 4, page 319-344
- ISSN: 0399-0559

## Access Full Article

top## Abstract

top## How to cite

topBaltz, Andreas, and Srivastav, Anand. "Fast approximation of minimum multicast congestion – Implementation VERSUS Theory." RAIRO - Operations Research 38.4 (2010): 319-344. <http://eudml.org/doc/105318>.

@article{Baltz2010,

abstract = {
The problem of minimizing the maximum edge congestion in a multicast
communication network generalizes the well-known NP-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)(rOPT + exp(1)lnm)-approximation can be computed in
O(kmε-2lnklnm) 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.
},

author = {Baltz, Andreas, Srivastav, Anand},

journal = {RAIRO - Operations Research},

keywords = {Combinatorial optimization; approximation algorithms.; approximation algorithms},

language = {eng},

month = {3},

number = {4},

pages = {319-344},

publisher = {EDP Sciences},

title = {Fast approximation of minimum multicast congestion – Implementation VERSUS Theory},

url = {http://eudml.org/doc/105318},

volume = {38},

year = {2010},

}

TY - JOUR

AU - Baltz, Andreas

AU - Srivastav, Anand

TI - Fast approximation of minimum multicast congestion – Implementation VERSUS Theory

JO - RAIRO - Operations Research

DA - 2010/3//

PB - EDP Sciences

VL - 38

IS - 4

SP - 319

EP - 344

AB -
The problem of minimizing the maximum edge congestion in a multicast
communication network generalizes the well-known NP-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)(rOPT + exp(1)lnm)-approximation can be computed in
O(kmε-2lnklnm) 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.

LA - eng

KW - Combinatorial optimization; approximation algorithms.; approximation algorithms

UR - http://eudml.org/doc/105318

ER -

## References

top- 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 Machinery44 (1997) 486–504. Zbl0890.68014
- 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.
- 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. Zbl1137.90014
- A.V. Goldberg, A natural randomization strategy for multicommodity flow and related algorithms. Inform. Process. Lett.42 (1992) 249–256. Zbl0773.90026
- 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. Zbl0911.90153
- 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. Zbl0808.90105
- 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.
- 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).
- 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. Zbl0809.68077
- 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. Zbl0826.68055
- D.W. Matula and F. Shahrokhi, The maximum concurrent flow problem. J. Association Computing Machinery37 (1990) 318–334. Zbl0696.68071
- K. Mehlhorn, A faster approximation algorithm for the Steiner problem in graphs. Inform. Process. Lett.27 (1998) 125–128. Zbl0635.68071
- S. Plotkin, D. Shmoys and E. Tardos, Fast approximation algorithms for fractional packing and covering problems. Math. Oper. Res.20 (1995) 257–301. Zbl0837.90103
- T. Radzik, Fast deterministic approximation for the multicommodity flow problem. Math. Prog.78 (1997) 43–58. Zbl0893.90057
- P. Raghavan, Probabilistic construction of deterministic algorithms: Approximating packing integer programs. J. Comp. Syst. Sci.38 (1994) 683–707.
- A. Srivastav and P. Stangier, On complexity, representation and approximation of integral multicommodity flows. Discrete Appl. Math.99 (2000) 183–208. Zbl0951.68048
- S. Vempala and B. Vöcking, Approximating Multicast Congestion, in Proc. 10th ISAAC, Chennai, India (1999) 367–372. Zbl0973.90086
- 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. Zbl0957.68084

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.