## Primal-dual RNC approximation algorithms for set cover and covering integer programs.(English)Zbl 0914.68096

### MSC:

 68W15 Distributed algorithms

### Keywords:

algorithms; set cover; primal-dual; parallel; approximation; voting lemmas
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### References:

 [1] B. Berger, J. Rompel, and P. Shor, Efficient NC algorithms for set cover with applications to learning and geometry, in Proc. 30th IEEE Symposium on the Foundations of Computer Science, 1989, pp. 54-59. [2] Chvátal, V., A greedy heuristic for the set‐covering problem, Math. Oper. Res., 4, 233-235 (1979) · Zbl 0443.90066 [3] Dobson, Gregory, Worst‐case analysis of greedy heuristics for integer programming with nonnegative data, Math. Oper. Res., 7, 515-531 (1982) · Zbl 0498.90061 [4] U. Feige, A threshold of $$\lnn$$ for approximating set cover, in Proc. 28th ACM Symposium on the Theory of Computing, 1996, pp. 312-318. · Zbl 0922.68067 [5] Johnson, DavidApproximation algorithms for combinatorial problemsJ. Comput. System Sci.91974256278Fifth Annual ACM Symposium on the Theory of Computing (Austin, Tex., 1973) [6] R. M. Karp, Reducibility among combinatorial problems, in Complexity of Computer Computations, R. E. Miller and J. W. Thatcher, eds., Plenum Press, New York, 1972, pp. 85-103. · Zbl 1467.68065 [7] M. Luby and N. Nisan, A parallel approximation algorithm for positive linear programming, in Proc. 25th ACM Symposium on Theory of Computing, 1993, pp. 448-457. · Zbl 1310.68224 [8] Lovász, L., On the ratio of optimal integral and fractional covers, Discrete Math., 13, 383-390 (1975) · Zbl 0323.05127 [9] Leighton, F.Introduction to parallel algorithms and architecturesMorgan Kaufmann1992xx+831Arrays, trees, hypercubes [10] C. Lund and M. Yannakakis, On the hardness of approximating minimization problems, in Proc. 25th ACM Symposium on Theory of Computing, 1993, pp. 286-293. · Zbl 1310.68094 [11] Plotkin, SergeShmoys, DavidTardos, ÉvaFast approximation algorithms for fractional packing and covering problemsIEEE Comput. Soc. PressLos Alamitos, CA1991495504 [12] Raghavan, PrabhakarProbabilistic construction of deterministic algorithms: approximating packing integer programsJ. Comput. System Sci.371988130143Twenty‐Seventh Annual IEEE Symposium on the Foundations of Computer Science (Toronto, ON, 1986)
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