Abstract
In this paper we demonstrate a general method of designing constant-factor approximation algorithms for some discrete optimization problems with cardinality constraints. The core of the method is a simple deterministic (“pipage”) procedure of rounding of linear relaxations. By using the method we design a (1 − (1 − 1/k)k)-approximation algorithm for the maximum coverage problem where k is the maximum size of the subsets that are covered, and a 1/2-approximation algorithm for the maximum cut problem with given sizes of parts in the vertex set bipartition. The performance guarantee of the former improves on that of the well-known (1 − e −1)-greedy algorithm due to Cornuejols, Fisher and Nemhauser in each case of bounded k. The latter is, to the best of our knowledge, the first constant-factor algorithm for that version of the maximum cut problem.
This research was partially supported by the Russian Foundation for Basic Research, grant 97-01-00890
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References
N. Alon and J. H. Spenser, The probabilistic method, John Wiley and Sons, New York, 1992.
G. Cornuejols, M. L. Fisher and G. L. Nemhauser, Location of bank accounts to optimize float: an analytic study exact and approximate algorithms, Management Science 23 (1977) 789–810.
G. Cornuejols, G. L. Nemhauser and L. A. Wolsey, Worst-case and probabilistic analysis of algorithms for a location problem, Operations Research 28 (1980) 847–858.
U. Feige, A threshold of ln n for approximating set cover, J. of ACM. 45 (1998) 634–652.
A. Frieze and M. Jerrum, Improved approximation algorithms for MAX k-CUT and MAX BISECTION, Algorithmica 18 (1997) 67–81.
M. X. Goemans and D. P. Williamson, New 3/4-approximation algorithms for MAX SAT, SIAM J. Discrete Math. 7 (1994) 656–666.
N. Guttmann-Beck and R. Hassin, Approximation algorithms for min-sum p-clustering, Discrete Appl. Math. 89 (1998) 125–142.
N. Guttmann-Beck and R. Hassin, Approximation algorithms for minimum K-cut, to appear in Algorithmica.
D. S. Hochbaum, Approximation algorithms for the set covering and vertex cover problems, SIAM J. on Computing 11 (1982) 555–556.
D. S. Hochbaum, Approximating covering and packing problems: Set Cover, Vertex Cover, Independent Set, and related problems, in: D. S. Hochbaum, ed., Approximation algorithms for NP-hard problems (PWS Publishing Company, New York, 1997) 94–143.
S. Khuller, A. Moss and J. Naor, The budgeted maximum coverage problem, to appear in Inform. Proc. Letters.
S. Sahni, Approximate algorithms for the 0–1 knapsack problem, J. of ACM 22 (1975) 115–124.
L. A. Wolsey, Maximizing real-valued submodular functions: primal and dual heuristics for location problems, Math. Oper. Res. 7 (1982) 410–425.
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© 1999 Springer-Verlag Berlin Heidelberg
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Ageev, A.A., Sviridenko, M.I. (1999). Approximation Algorithms for Maximum Coverage and Max Cut with Given Sizes of Parts. In: Cornuéjols, G., Burkard, R.E., Woeginger, G.J. (eds) Integer Programming and Combinatorial Optimization. IPCO 1999. Lecture Notes in Computer Science, vol 1610. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48777-8_2
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DOI: https://doi.org/10.1007/3-540-48777-8_2
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