Abstract
We investigate how the recently developed different approaches to generate randomized roundings satisfying disjoint cardinality constraints behave when used in two classical algorithmic problems, namely low-congestion routing in networks and max-coverage problems in hypergraphs. Based on our experiments, we also propose and investigate the following new ideas. For the low-congestion routing problems, we suggest to solve a second LP, which yields the same congestion, but aims at producing a solution that is easier to round. For the max-coverage instances, observing that the greedy heuristic also performs very good, we develop hybrid approaches, in the form of a strengthened method of derandomized rounding, and a simple greedy/rounding hybrid using greedy and LP-based rounding elements. Experiments show that these ideas significantly reduce the rounding errors.
For an important special case of max-coverage, namely unit disk max-domination, we also develop a PTAS. However, experiments show it less competitive than other approaches, except possibly for extremely high solution qualities.
Supported by the German Science Foundation (DFG) via its priority program (SPP) 1307 “Algorithm Engineering”, grant DO 749/4-2.
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References
Ageev, A.A., Sviridenko, M.: Pipage rounding: A new method of constructing algorithms with proven performance guarantee. J. Comb. Optim. 8, 307–328 (2004)
Arora, S.: Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems. J. ACM 45, 753–782 (1998)
Cornuejols, G., Fisher, M.L., Nemhauser, G.L.: Location of Bank Accounts to Optimize Float: An Analytic Study of Exact and Approximate Algorithms. Management Science 23, 789–810 (1977)
Doerr, B.: Generating randomized roundings with cardinality constraints and derandomizations. In: Durand, B., Thomas, W. (eds.) STACS 2006. LNCS, vol. 3884, pp. 571–583. Springer, Heidelberg (2006)
Doerr, B., Wahlström, M.: Randomized rounding in the presence of a cardinality constraint. In: ALENEX 2009, pp. 162–174 (2009)
Gandhi, R., Khuller, S., Parthasarathy, S., Srinivasan, A.: Dependent rounding in bipartite graphs. In: FOCS 2002, pp. 323–332 (2002)
Gandhi, R., Khuller, S., Parthasarathy, S., Srinivasan, A.: Dependent rounding and its applications to approximation algorithms. J. ACM 53, 324–360 (2006)
Glaßer, C., Reith, S., Vollmer, H.: The complexity of base station positioning in cellular networks. Discrete Applied Mathematics 148, 1–12 (2005)
Karp, R.M., Leighton, F.T., Rivest, R.L., Thompson, C.D., Vazirani, U.V., Vazirani, V.V.: Global wire routing in two-dimensional arrays. Algorithmica 2, 113–129 (1987)
Khuller, S., Moss, A., Naor, J.S.: The budgeted maximum coverage problem. Information Processing Letters 70, 39–45 (1999)
Kleinberg, J.: Approximation Algorithms for Disjoint Paths Problems. PhD thesis, MIT (1996)
Kochetov, Y., Ivanenko, D.: Computationally difficult instances for the uncapacitated facility location problem. In: Proc. of the 5th Metaheuristic Conf., MIC 2003 (2003)
Kratica, J., Toic, D., Filipovi, V., Ljubi, I.: Solving the simple plant location problem by genetic algorithm. RAIRO Oper. Res. 35, 127–142 (2001)
L.A.N.Lorena-instancias, http://www.lac.inpe.br/~lorena/instancias.html
Masuyama, S., Ibaraki, T., Hasegawa, T.: Computational complexity of the m-center problems on the plane. Trans. of the Inst. of Electron. and Commun. Eng. of Japan. Sect. E 64, 57–64 (1981)
OR-Library, http://people.brunel.ac.uk/~mastjjb/jeb/info.html
Pereira, M.A., Lorena, L.A.N., Senne, E.L.F.: A column generation approach for the maximal covering location problem. Int. Trans. in Oper. Res. 14, 349–364 (2007)
Raghavan, P.: Probabilistic construction of deterministic algorithms: Approximating packing integer programs. J. Comput. Syst. Sci. 37, 130–143 (1988)
Raghavan, P., Thompson, C.D.: Randomized rounding: A technique for provably good algorithms and algorithmic proofs. Combinatorica 7, 365–374 (1987)
Srinivasan, A.: Distributions on level-sets with applications to approximations algorithms. In: FOCS 2001, pp. 588–597 (2001)
UflLib, http://www.mpi-inf.mpg.de/departments/d1/projects/benchmarks/UflLib/
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Doerr, B., Künnemann, M., Wahlström, M. (2010). Randomized Rounding for Routing and Covering Problems: Experiments and Improvements. In: Festa, P. (eds) Experimental Algorithms. SEA 2010. Lecture Notes in Computer Science, vol 6049. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13193-6_17
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