Approximation algorithms for submodular set cover with applications

IEICE Transactions on Information and Systems

Volumn E83-D, Issue 3, 2000, Pages 480-487

  Fujito, Toshihiro ^a  

^a NAGOYA UNIVERSITY   (Japan)

Author keywords

Approximation algorithms; Greedy heuristics; Set cover; Submodular function

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL COMPLEXITY; HEURISTIC METHODS; LINEAR PROGRAMMING; SET THEORY;

APPROXIMATION ALGORITHMS; GREEDY HEURISTICS; SUBMODULAR SET COVER;

ALGORITHMS;

EID: 0034157028     PISSN: 09168532     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (34)

1. R. Bar-Yehuda Using homogeneous weights for approximating the partial cover problem Proc. 10th Annual ACM-SIAM Symp. on Discrete Algorithms pp.71-75 1999.
2. R. Bar-Yehuda and S. Even A local-ratio theorem for approximating the weighted vertex cover problem Annals of Discrete Mathematics vol.25 pp.27-4G North-Holland 1985.
3. N.H. Bshouty and L. Burroughs Massaging a linear programming solution to give a 2-approximation for a generalization of the vertex cover problem Proc. 15th Symp. on Theoretical Aspects of Computer Science pp.298-308 1998.
4. V. Chvatal A greedy heuristic for the set-covering problem Mathematics of Operations Research vol.4 no.3 pp.233-235 1979.
5. G. Dobson Worst-case analysis of greedy heuristics for integer programming with nonnegative data Mathematics of Operations Research vol.7 no.4 pp.515-531 1982.
6. J. Edmonds Submodular functions matroids and certain polyhedra in Combinatorial Structures and Their Applications eds. R. Guy H. Hanani N. Sauer and J. Schönheim pp.69-87 1970.
7. U. Feige A threshold of Inn for approximating set cover Proc. 28th Annual ACM Symp. on Theory of Computing pp.314-318 199G.
8. S. Fujishige Submodular functions and optimization Annals of Discrete Mathematics vol.47 North Holland 1991.
9. T. Fujito A unified local ratio approximation of nodedeletion problems Proc. 4th European Symp. on Algorithms pp.167-178 1996.
10. T. Fujito. Approximating node-deletion problems for matroidal properties J. Algorithms vol.31 pp.211-227 1999.
11. M. Grötschel L. Lovâsz and A. Schrijver The ellipsoid method and its consequences in combinatorial optimization Combinatorica vol.1 pp.169-197 1988. [12] M. Grötschel L. Lovâsz and A. Schrijver Geometric methods in combinatorial optimization in Progress in Combinatorial Optimization éd. W.R. Pulleyblank pp.167-183 Academic Press 1984.
12. J. Hâstad 'Some optimal in-approximability results Proc. 29th Annual ACM Symp. on Theory of Computing pp.1-10 1997.
13. D.S. Hochbaum Approximation algorithms for the set covering and vertex cover problems SIAM J. Computing vol.11 pp.555-556 1982.
14. D.S. Hochbaum The t-vertex cover problem: Extending the half integrality framework with budget constraints Proc. APPROX'98 1st International Workshop on Approximation Algorithms for Combinatorial Optimization Problems pp.111-122 1998.
15. [1C] D.S. Johnson Approximation algorithms for combinatorial problems J. Comput. Syst. Sci. vol.9 pp.256-278 1974.
16. R.M. Karp Rcducibility among combinatorial problems in Complexity of Computer Computations cds. R.E. Miller and J.W. Thatcher pp.85-103 Plenum Press New York 1972.
17. M.J. Kearns The Computational Complexity of Machine Learning MIT Press Cambridge MA 1990.
18. L. Lovasz On the ratio of optimal integral and fractional covers Discrete Mathematics vol.13 pp.383-390 1975.
19. L. Lovasz Submodular functions and convexity in Mathematical Programming -The State of the Art eds. A. Bachern M. Grötschel and B. Körte pp.235-257 Springer 1983.
20. J.M. Lewis and M. Yannakakis The node-deletion problem for hereditary properties is NP-complete J. Comput. Syst. Sci. vol.20 pp.219-230 1980.
21. C. Lund and M. Yannakakis ''The approximation of maximum subgraph problems Proc. 20th International Colloquium on Automata Languages and Programming pp.4051 1993.
22. B. Monien and E. Speckenmeyer Ramsey numbers and an approximation algorithm for the vertex cover problem Acta Informatica vol.22 pp.115-123 1985.
23. H. Nagamochi and T. Ibaraki A note on minimizing submodular functions Inf. Process. Lett. vol.67 pp.239-244 1998.
24. G.L. Kernhäuser L.A. Wolsey and M.L. Fisher An analysis of approximations for maximizing submodular set functions .- I Math. Program. vol.14 pp.265-294 1978.
25. G.L.' Kernhäuser and L.A. Wolsey Maximizing submodular set functions: Formulations and analysis of algorithms Studies on Graphs and Discrete Programming pp.279-301 North-Holland 1981.
26. G.L. Nemhauser and L.A. Wolsey Integer and Combinatorial Optimization Wiley New York 1988.
27. M. Queyranne A combinatorial algorithm for minimizing symmetric submodular function Proc. 6th Annual ACMSIAM Symp. on Discrete Algorithms pp.98-101 1995.
28. R. Rado A note on independence functions Proc. London Mathematical Society vol.7 pp.300-320 1957.
29. A. Recski Matroid Theory and its Applications SpringerVerlag Berlin 1989.
30. R. Raz and S. Safra A sub constant error probability low degree test and a sub constant error probability PCP characterization of NP Proc. 29th ACM Symp. on Theory of Computing pp.475-484 1995.
31. P. Slavîk Improved performance of the greedy algorithm for partial cover Inf. Process. Lett. vol.64 no.5 pp.251254 1997.
32. D.J.A. Welsh Matroid Theory Academic Press London 1976.
33. L.A. Wolsey An analysis of the greedy algorithm for the submodular set covering problem Combinatorica vol.2 no.4 pp.385-393 1982.
34. L.A. Wolsey Maximising real-valued submodular functions: Primal and dual heuristics for location problems Mathematics of Operations Research vol.7 no.3 pp.410425 1982.