Abstract
This paper proposes a new method of solving the argument reduction problem. Our method is different to the classical approach using the greedy algorithm, independently invented by Lovasz, Johnson, and Chvatal. However, sometimes the classical method does not produce minimal sets in the sense of cardinality. According to the results of computer tests, better results can be achieved by application of our method in combination with the classical method. Therefore, improvements are found in the quality of solutions when it is applied as a post-processing method.
Research partly supported by the grant from the State Committee for Scientific Research. Decision no. 55/E-82/SPB/5.PR UE/DZ 385/2003–2005 of 16.07.2003
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References
Aussiello G, Crescenzi P, Gambosi G, Kann V, Marchetti-Spaccamela A, Protasi M, (1999) “Complexity and Approximation”, Springer
Ballobas B (1986) “Combinatorics, Set Systems, Hypergraphs, Families of Vectors and Combinatorial Probability”, Cambridge University Press
Berge C (1989) “Hypergraphs, Combinatorics of Finite Sets”, North-Holland
Berger B, Rompel J (1994) “Effcient NC Algorithms for Set Cover with Applications to Learning and Geometry”, Journal of Computer and System Sciences 49, 454–477
Blot J, Hemandez de la Vega W, Paschos V Th, Saad R (1995) “Average case analysis of greedy algorithms for optimisation problems on set problems”, Theoretical Computer Science 147, 267–288
Buciak P, Łuba T, Niewiadomski H, Pleban M, Sapiecha P, Selvaraj H (2002): Decomposition and Argument Reduction of Neural Networks, IEEE Sixth International Conference on Neural Networks and Soft Computing (ICNNSC’02), Poland, June 11–15, 2002
Chvatal V (1979) “A greedy heuristic for the set-covering problem”, Mathematics and Operations Research, 4, 233–235
Feige U (1998), “A Threshold of ln(n) for Approximating Set Cover”, Journal of the ACM
Hromkovic J (2001) “Algorithmics for Hard Problems”, Springer
Hochbaum D S (Ed.) (1997) Approximation Algorithms for NP-hard Problems, PWS Publishing Company
Korte B, Vygen J (2000) “Combinatorial Optimization, Theory and Algorithms”, Springer
Johnson D S (1974) “Approximation Algorithms for Combinatorial Problems”, Journal of Computer and System Sciences, 9, 256–278
Lovasz L (1975) “On the ratio of optimal integral and fractional covers”, Discrete Mathematics 13 383–390
Lund C, Yannakakis M (1994) “On the Hardness of Approximating Minimization Problems”, Journal of the ACM
de Micheli G (1994) “Synthesis and Optimization of Digital Circuits”, McGraw-Hill Inc.
Motvani R (1992) “Lecture Notes on Approximation Algorithms-Volume F”, Stanford University
Niewiadomski H, Buciak P, Pleban M, Selvaraj H, Sapiecha P, Łuba T (2002) Decomposition of Large Neural Networks, Proceedings of the IASTED International Conference, Applied Informatics, International Symposium on Artificial Intelligence and Applications, pp. 165–170, Insbruck, Austria, February 18–21, 2002
Pleban M, Niewiadomski H, Buciak P, Sapiecha P, Yanushkevich S, Shmerko V (2002) Argument reduction algorithms for multi-valued relations, IASTED International Conference on Artificial Intelligence and Soft Computing (ASC 2002), pp. 609–614, Banff, Canada, July 17–19, 2002
Skowron A, Rauszer C (1992) “The discemibility matrices and functions in information systems”, in: R. Slowinski (Ed.), “Intelligent Decision Support. Handbook of Applications and Advances on the Rough Set Theory”, Kluwer
Slavik P (1996) “A Tight Analysis of the Greedy Algorithm for Set Cover”, STOC’96, USA
Srinivasan A (1995) “Improved Approximation Guamatees for Packing and Covering Integer Programs”, DIMACS TR.
Vazirani V (1997), “Approximation Algorithms”, Lecture Notes 1997, Georgia Institute of Technology
Williamson D (1999) “Lecture Notes on Approximation Algorithms”, IBM Research Report, RC 21409,02/17/1999
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Kułaga, P., Sapiecha, P., S#x0119;p, K. (2005). Approximation Algorithm for the Argument Reduction Problem. In: Kurzyński, M., Puchała, E., Woźniak, M., żołnierek, A. (eds) Computer Recognition Systems. Advances in Soft Computing, vol 30. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-32390-2_27
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DOI: https://doi.org/10.1007/3-540-32390-2_27
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