Greedy δ-Approximation algorithm for covering with arbitrary constraints and submodular cost

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 5555 LNCS, Issue PART 1, 2009, Pages 634-652

  Koufogiannakis, Christos ^a   Young, Neal E ^a  

^a University of California Riverside   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION RATIOS; ARBITRARY CONSTRAINTS; CACHE SIZE; CACHING STRATEGY; COMPETITIVE ALGORITHMS; COVERING PROBLEMS; HARDWARE CONFIGURATIONS; LINEAR PROGRAMS; NP-HARD; ON-LINE ALGORITHMS; ONLINE VERSIONS; SET COVER; SUBMODULAR; UPPER BOUND; VERTEX COVER;

COMPUTATIONAL COMPLEXITY; INTEGER PROGRAMMING; LINGUISTICS; TRANSLATION (LANGUAGES);

APPROXIMATION ALGORITHMS;

EID: 70449083285     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-02927-1_53     Document Type: Conference Paper

References (53)

1. Albers, S.: On generalized connection caching. Theory of Computing Systems 35(3), 251-267 (2002)
2. Bansal, N., Buchbinder, N., Naor, J.: A primal-dual randomized algorithm for weighted paging. In: The forty-third IEEE symposium on Foundations Of Computer Science, pp. 507-517 (2007)
3. Bansal, N., Buchbinder, N., Naor, J.S.: Randomized competitive algorithms for generalized caching. In: The fourtieth ACM Symposium on Theory Of Computing, pp. 235-244. ACM, New York (2008)
4. Bar-Yehuda, R.: One for the price of two: A unified approach for approximating covering problems. Algorithmica 27(2), 131-144 (2000)
5. Bar-Yehuda, R., Bendel, K., Freund, A., Rawitz, D.: Local ratio: a unified framework for approximation algorithms. ACM Computing Surveys 36(4), 422-463 (2004)
6. Bar-Yehuda, R., Even, S.: A linear-time approximation algorithm for the weighted vertex cover problem. J. Algorithms 2(2), 198-203 (1981)
7. Bar-Yehuda, R., Even, S.: A local-ratio theorem for approximating the weighted vertex cover problem. Annals of Discrete Mathematics 25(27-46), 50 (1985)
8. Bar-Yehuda, R., Rawitz, D.: Efficient algorithms for integer programs with two variables per constraint 1. Algorithmica 29(4), 595-609 (2001)
9. Bar-Yehuda, R., Rawitz, D.: On the equivalence between the primal-dual schema and the local-ratio technique. SIAM Journal on Discrete Mathematics 19(3), 762-797 (2005)
10. Bertsimas, D., Vohra, R.: Rounding algorithms for covering problems. Mathematical Programming: Series A and B 80(1), 63-89 (1998)
11. Borodin, A., Cashman, D., Magen, A.: How well can primal-dual and local-ratio algorithms perform? In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 943-955. Springer, Heidelberg (2005)
12. Borodin, A., El-Yaniv, R.: Online computation and competitive analysis. Cambridge University Press, New York (1998)
13. Buchbinder, N., Naor, J.: Online primal-dual algorithms for covering and packing problems. In: Brodai, G.S., Leonardi, S. (eds.) ESA 2005. LNCS, vol. 3669, pp. 689-701. Springer, Heidelberg (2005)
14. Cao, P., Irani, S.: Cost-aware www proxy caching algorithms. In: the USENIX Symposium on Internet Technologies and Systems on USENIX Symposium on Internet Technologies and Systems table of contents, pp. 18-18 (1997)
15. Carr, R.D., Fleischer, L.K., Leung, V.J., Phillips, C.A.: Strengthening integrality gaps for capacitated network design and covering problems. In: The eleventh ACM-SIAM Symposium On Discrete Algorithms, Philadelphia, PA, USA, pp. 106-115. Society for Industrial and Applied Mathematics (2000)
16. Chrobak, M., Karloff, H., Payne, T., Vishwanathan, S.: New results on server problems. SIAM J. Discrete Math. 4(2), 172-181 (1991)
17. Chvatal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4, 233-235 (1979)
18. Cohen, E., Kaplan, H., Zwick, U.: Connection caching. In: The thirty-first ACM Symposium on Theory Of Computing, pp. 612-621 (1999)
19. Cohen, E., Kaplan, H., Zwick, U.: Connection caching under various models of communication. In: The twelfth ACM Symposium on Parallel Algorithms and Architectures, pp. 54-63 (2000)
20. Cohen, E., Kaplan, H., Zwick, U.: Connection caching: Model and algorithms. Journal of Computer and System Sciences 67(1), 92-126 (2003)
21. Dinur, I., Safra, S.: On the hardness of approximating minimum vertex cover. Annals of Mathematics, 162 (2005)
22. Dobson, G.: Worst-case analysis of greedy heuristics for integer programming with nonneg-ative data. Mathematics of Operations Research 7(4), 515-531 (1982)
23. Fiat, A., Karp, R.M., Luby, M., McGeoch, L.A., Sleator, D.D., Young, N.E.: Competitive paging algorithms. J. Algorithms 12, 685-699 (1991)
24. Fisher, M.L., Wolsey, L.A.: On the Greedy Heuristic for Continuous Covering and Packing Problems. SIAM Journal on Algebraic and Discrete Methods 3, 584-591 (1982)
25. Gonzales, T. (ed.): Approximation Algorithms and Metaheuristics, ch 4. (Greedy Methods). Tylor and Francis Books, CRC Press (2007)
26. Hall, N.G., Hochbaum, D.S.: A fast approximation algorithm for the multicovering problem. Discrete Applied Mathematics 15(1), 35-40 (1986)
27. Halldorsson, M.M., Radhakrishnan, J.: Greed is good: Approximating independent sets in sparse and bounded-degree graphs. In: The twenty-sixth ACM Symposium on Theory Of Computing, pp. 439-448 (1994)
28. Halperin, E.: Improved approximation algorithm for the vertex cover problem in graphs and hypergraphs. SIAM Journal on Computing 31(5), 1608-1623 (2002)
29. Hastad, J.: Some optimal inapproximability results. Journal of the ACM 48(4), 798-859 (2001)
30. Hayrapetyan, A., Swamy, C., Tardos, E.: Network design for information networks. In: The sixteenth ACM-SIAM Symposium On Discrete Algorithms, pp. 933-942 (2005)
31. Hochbaum, D.S.: Approximation algorithms for the set covering and vertex cover problems. SIAM Journal on Computing 11, 555-556 (1982)
32. Hochbaum, D.S.: Efficient bounds for the stable set, vertex cover, and set packing problems. Discrete Applied Mathematics 6, 243-254 (1983)
33. Hochbaum, D.S.: Approximation algorithms for the set covering and vertex cover problems. SIAM Journal on Computing 11, 555 (1982)
34. Hochbaum, D.S.: Approximation algorithms for NP-hard problems. PWS Publishing Co., Boston (1996)
35. Johnson, D.S.: Approximation algorithms for combinatorial problems. In: The fifth ACM Symposium On Theory Of Computing, vol. 25, pp. 38-49 (1973)
36. Karlin, A.R., Manasse, M.S., Rudolph, L., Sleator, D.D.: Competitive snoopy caching. Al-gorithmica 3, 77-119 (1988)
37. Khot, S., Regev, O.: Vertex cover might be hard to approximate to within 2-e. Journal of Computer and System Sciences 74, 335-349 (2008)
38. Kolliopoulos, S.G., Young, N.E.: Approximation algorithms for covering/packing integer programs. Journal of Computer and System Sciences 71(4), 495-505 (2005)
39. Koufogiannakis, C., Young, N.E.: Distributed and parallel algorithms for weighted vertex cover and other covering problems. In: The twenty-eighth ACM symposium Principles of Distributed Computing (2009)
40. Lotker, Z., Patt-Shamir, B., Rawitz, D.: Rent, lease or buy: Randomized algorithms for mul-tislope ski rental. In: The twenty fifth Symposium on Theoretical Aspects of Computer Science, pp. 503-514 (2008)
41. Lotker, Z., Patt-Shamir, B., Rawitz, D.: Rent, lease or buy: Randomized algorithms for mul-tislope ski rental. In: Albers, S., Weil, P. (eds.) STACS, Internationales Begegnungs- und Forschungszentrum fuer Informatik (IBFI), Schloss Dagstuhl, Germany. Dagstuhl Seminar Proceedings, vol. 08001, pp. 503-514 (2008)
42. Lovasz, L.: On the ratio of optimal integral and fractional covers. Discrete Math. 13, 383-390 (1975)
43. McGeoch, L.A., Sleator, D.D.: A strongly competitive randomized paging algorithm. Algorithmica 6(1), 816-825 (1991)
44. Monien, B., Speckenmeyer, E.: Ramsey numbers and an approximation algorithm for the vertex cover problem. Acta Informatica 22, 115-123 (1985)
45. Orlin, J.B.: A faster strongly polynomial time algorithm for submodular function minimization. In: Fischetti, M., Williamson, D.P. (eds.) IPCO 2007. LNCS, vol. 4513, pp. 240-251. Springer, Heidelberg (2007)
46. Pritchard, D.: Approximability of sparse integer programs. Technical report, arxiv.org (2009), http://arxiv.org/abs/0904.0859
47. Raghavan, P., Snir, M.: Memory versus randomization in on-line algorithms. IBM Journal of Research and Development 38(6), 683-707 (1994)
48. Sleator, D.D., Tarjan, R.E.: Amortized efficiency of list update and paging rules. Communications of the ACM 28(2), 202-208 (1985)
49. Srinivasan, A.: Improved approximation guarantees for packing and covering integer programs. SIAM Journal on Computing 29, 648-670 (1999)
50. Srinivasan, A.: New approaches to covering and packing problems. In: The twelveth ACM-SIAM Symposium On Discrete Algorithms, pp. 567-576 (2001)
51. Vazirani, V.V.: Approximation algorithms. Springer, Heidelberg (2001)
52. Young, N.E.: The k-server dual and loose competitiveness for paging. Algorithmica 11, 525-541 (1994)
53. Young, N.E.: On-line file caching. Algorithmica 33(3), 371-383 (2002)