Geodesic
Investigation of integer programming problems by means of unimodular transformations and regular partitions
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 2, pp. 193-202

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Investigations of questions in integer linear programming are carried out concerned with the joint application of unimodular transformations and the method of regular partitions for changing the structure of problems and increasing the efficiency of algorithms. Main results are obtained for the knapsack problem and some of its generalizations based on an $L$-partition. Families of problems with $L$-coverings of exponential cardinality are presented, and unimodular transformations that improve their structure are constructed. New estimates for the number of iterations are described for $L$-class enumeration algorithms.
Keywords: integer programming, unimodular transformation, regular partition, $L$-class enumeration algorithm.
Mots-clés : $L$-partition 
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     title = {Investigation of integer programming problems by means of unimodular transformations and regular partitions},
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A. A. Kolokolov; T. G. Orlovskaya. Investigation of integer programming problems by means of unimodular transformations and regular partitions. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 2, pp. 193-202. http://geodesic.mathdoc.fr/item/TIMM_2013_19_2_a17/