Hard equality constrained integer knapsacks

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 2337 LNCS, Issue , 2002, Pages 350-366

  Aardal, Karen ^a   Lenstra, Arjen K ^b,c  

^a UTRECHT UNIVERSITY   (Netherlands)

^b Emerging Technology   (United States)

^c EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

COMBINATORIAL OPTIMIZATION; INFORMATION DISSEMINATION;

ALMOST TRIVIAL; COMPUTATIONAL STUDIES; FEASIBILITY PROBLEM; NONNEGATIVE INTEGERS; POSITIVE INTEGERS;

INTEGER PROGRAMMING;

EID: 84868682383     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-47867-1_25     Document Type: Conference Paper

References (21)

1. Aardal K., Bixby R.E., Hurkens C.A.J., Lenstra A.K., Smeltink J.W. (1999) Market Split and Basis Reduction: Towards a Solution of the Cornuéjols-Dawande Instances. In: Cornuéjols G., Burkard R.E., Woeginger G.J. (eds.) Integer Programming and Combinatorial Optimization, 7th International IPCO Conference. Lecture Notes in Computer Science 1610. Springer-Verlag, Berlin, Heidelberg, 1-16
2. Aardal K., Hurkens, C.A.J., Lenstra A.K. (2000) Solving a system of diophantine equations with lower and upper bounds on the variables. Mathematics of Operations Research 25:427-442
3. Brauer A. (1942) On a problem of partitions. American Journal of Mathematics 64:299-312
4. Brauer A., Shockley J.E. (1962) On a problem of Frobenius. Journal für reine und angewandte Mathematik 211:399-408
5. Cook W., Rutherford T., Scarf H. E., Shallcross D. (1993) An implementation of the generalized basis reduction algorithm for integer programming. ORSA Journal on Computing 5:206-212
6. Cornuéjols G., Dawande M. (1998) A class of hard small 0-1 programs. In: Bixby R.E., Boyd E.A., Ríos-Mercado R.Z. (eds.) Integer Programming and Combinatorial Optimization, 6th International IPCO Conference. Lecture Notes in Computer Science 1412. Springer-Verlag, Berlin Heidelberg, 284-293
7. Cornuéjols G., Urbaniak R., Weismantel R., Wolsey L.A. (1997) Decomposition of integer programs and of generating sets. In: Burkard R.E., Woeginger G.J. (eds.) Algorithms - ESA '97. Lecture Notes in Computer Science 1284. Springer-Verlag, Berlin, Heidelberg, 92-103
8. Erdös P., Graham R.L. (1972) On a linear diophantine problem of Frobenius. Acta Arithmetica 21:399-408
9. Greenberg H. (1988) Solution to a linear Diophantine equation for nonnegative integers. Journal of Algorithms 9:343-353
10. Hungerford T.W. (1996) Algebra; corrected eighth printing. Springer-Verlag, New York
11. Kannan R. (1991) Lattice translates of a polytope and the Frobenius Problem. Combinatorica 12:161-177
12. Khinchine A. (1948) A quantitative formulation of Kronecker's theory of approximation (In Russian). Izvestiya Akademii Nauk SSR Seriya Matematika 12:113-122
13. Lenstra A.K., Lenstra H.W., Jr., Lovász L. (1982) Factoring polynomials with rational coefficients. Mathematische Annalen 261:515-534
14. Lenstra H.W., Jr., (1983) Integer programming with a fixed number of variables. Mathematics of Operations Research 8:538-548
15. Lovász L., Scarf H.E. (1992) The generalized basis reduction algorithm, Mathematics of Operations Research 17:751-764
16. Louveaux Q., Wolsey L.A. (2000) Combining problem structure with basis reduction to solve a class of hard integer programs. CORE Discussion Paper 2000/51, CORE, Université Catholique de Louvain, Louvain-la-Neuve, Belgium (to appear in Mathematics of Operations research)
17. Rödseth Ö.J. (1978) On a linear diophantine problem of Frobenius. Journal für reine und angewandte Mathematik 301:171-178
18. Schrijver A. (1986) Theory of linear and integer programming, Wiley, Chichester
19. Selmer E.S. (1977) On the linear diophantine problem of Frobenius. Journal für reine und angewandte Mathematik 93/294:1-17
20. Selmer E.S., Beyer Ö. (1978) On the linear diophantine problem of Frobenius in three variables. Journal für reine und angewandte Mathematik 301:161-170
21. Sylvester J.J., Curran Sharp W.J. (1884). [Problem] 7382. Mathematics from the Educational Times, with Additional Papers and Solutions 41:21