An approximation algorithm for the general max-min resource sharing problem

Mathematical Programming

Volumn 106, Issue 3, 2006, Pages 547-566

  Jansen, Klaus ^a  

^a UNIVERSITY OF KIEL   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; CONSTRAINT THEORY; ITERATIVE METHODS; OPTIMIZATION; PROBLEM SOLVING; SET THEORY;

APPROXIMATE BLOCK SOLVERS; C-APPROXIMATION ALGORITHM; LAGRANGIAN DECOMPOSITION;

ALGORITHMS;

EID: 33644538913     PISSN: 00255610     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10107-005-0669-1     Document Type: Article

References (24)

1. Aizatulin, M., Diedrich, F., Jansen, K.: Implementation of approximation algorithms for the max-min resource sharing problem. Unpublished manuscript
2. Blazewicz, J., Cellary, W., Slowinski, R., Weglarz, J.: Scheduling under resource constraints - deterministic models. Ann. Oper. Res. 7, 1986
3. Bienstock, D.: Potential function methods for approximately solving linear programming problems: Theory and practive, Kluwer, Boston, 2002
4. Caragiannis, I., Ferreira, A., Kaklamanis, C., Perennes, S., Rivano, H.: Fractional path coloring with applications to WDM networks, Proceedings 28th International Colloquium on Automata, Languages, and Programming, ICALP 2001, LNCS 2076, pp. 732-743
5. Charikar, M., Chekuri, C., Goel, A., Guha, S., Plotkin, S.: Approximating a finite metric by a small number of tree metrics. Proceedings 39th IEEE Symposium on Foundations of Computer Science, FOCS, 1998, pp. 379-388
6. Fleischer, L.: A fast approximation scheme for fractional covering problems with variable upper bounds, Proceedings of the 15th ACM-SIAM Symposium on Discrete Algorithms, SODA, 2004, pp. 1001-1010
7. Garg, N., Könemann, J.: Fast and simpler algorithms for multicommodity flow and other fractional packing problems. Proceedings 39th IEEE Symposium on Foundations of Computer Science, FOCS, 1998, pp. 300-309
8. Grigoriadis, M.D., Khachiyan, L.G.: Fast approximation schemes for convex programs with many blocks and coupling constraints. SIAM J. Optimization 4, 86-107 (1994)
9. Grigoriadis, M.D., Khachiyan, L.G.: Coordination complexity of parallel price-directive decomposition. Math. Oper. Res. 2, 321-340 (1996)
10. Grigoriadis, M.D., Khachiyan, L.G., Porkolab, L., Villavicencio, J.: Approximate max-min resource sharing for structured concave optimization. SIAM J. Optimization 41, 1081-1091 (2001)
11. Jansen, K.: Scheduling malleable parallel tasks: An asymptotic fully polynomial time approximation scheme. Algorithmica 39, 59-81 (2004)
12. Jansen, K.: Improved approximation algorithms for the general max-min resource sharing and fractional covering problem. Unpublished manuscript
13. Jansen, K., Porkolab, L.: On preemptive resource constrained scheduling: polynomial-time approximation schemes. Proceedings 9th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2002, LNCS 2337, pp. 329-349
14. Jansen, K., Zhang, H.: Approximation algorithms for general packing problems with modified logarithmic potential function. Proceedings 2nd IFIP International Conference on Theoretical Computer Science, TCS 2002, Kluwer Publisher, pp. 255-266
15. Kenyon C., Remila, E.: Approximate strip packing. Math. Oper. Res. 25, 645-656 (2000)
16. Klein, P., Young, N.: On the number of iterations for Dantzig-Wolfe optimization and packing-covering approximation algorithms. Proceedings 7th International Conference on Integer Programming and Combinatorial Optimization, IPCO 1999, LNCS 1610, pp. 320-327
17. Könemann, J. : Fast combinatorial algorithms for packing and covering problems, Diploma Thesis, Max-Planck-Institute for Computer Science Saarbrücken, 2000
18. Krause, K.L., Shen, V. Y., Schwetman, H.D.: Analysis of several task scheduling algorithms for a model of multiprogramming computer systems. J. ACM 22, 522-550 (1975) and Errata, J. ACM 24, 527 (1977)
19. Matsui, T.: Approximation algorithms for maximum independent set problems and fractional coloring problems on unit disk graphs. Proceedings Symposium on Discrete and Compuational Geometry 2000, LNCS 1763, pp. 194-200
20. Plotkin, S.A., Shmoys, D.B., Tardos, E.: Fast approximation algorithms for fractional packing and covering problems. Math. Oper. Res. 20, 257-301 (1995)
21. Schreinerman, E.R., Ullman, D.H.: Fractional Graph Theory: A Rational Approach to the Theory of Graphs, Wiley Interscience Series in Discrete Mathematics, 1997
22. Villavicencio, J., Grigoriadis, M.D.: Approximate Lagrangian decomposition with a modified Karmarkar logarithmic potential, Network Optimization. In: P. Pardalos, D.W. Hearn, W.W. Hager (eds.), Lecture Notes in Economics and Mathematical Systems 450, Springer, Berlin, 1997, pp. 471-485
23. Young, N.E.: Randomized rounding without solving the linear program. Proceedings 6th ACM-SIAM Symposium on Discrete Algorithms, SODA, 1995, pp. 170-178
24. Young, N.E.: Sequential and parallel algorithms for mixed packing and covering. Proceedings 42nd Annual IEEE Symposium on Foundations of Computer Science, FOCS 2001, pp. 538-546