An 0 ( n 3 ) worst case bounded special L P knapsack ( 0 - 1 ) with two constraints

Ruy E. Campello; Nelson Maculan

RAIRO - Operations Research - Recherche Opérationnelle (1988)

  • Volume: 22, Issue: 1, page 27-32
  • ISSN: 0399-0559

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Campello, Ruy E., and Maculan, Nelson. "An $0 (n^3)$ worst case bounded special $LP$ knapsack $(0-1)$ with two constraints." RAIRO - Operations Research - Recherche Opérationnelle 22.1 (1988): 27-32. <http://eudml.org/doc/104931>.

@article{Campello1988,
author = {Campello, Ruy E., Maculan, Nelson},
journal = {RAIRO - Operations Research - Recherche Opérationnelle},
keywords = {geometric complexity type proof; knapsack problem; side constraint},
language = {eng},
number = {1},
pages = {27-32},
publisher = {EDP-Sciences},
title = {An $0 (n^3)$ worst case bounded special $LP$ knapsack $(0-1)$ with two constraints},
url = {http://eudml.org/doc/104931},
volume = {22},
year = {1988},
}

TY - JOUR
AU - Campello, Ruy E.
AU - Maculan, Nelson
TI - An $0 (n^3)$ worst case bounded special $LP$ knapsack $(0-1)$ with two constraints
JO - RAIRO - Operations Research - Recherche Opérationnelle
PY - 1988
PB - EDP-Sciences
VL - 22
IS - 1
SP - 27
EP - 32
LA - eng
KW - geometric complexity type proof; knapsack problem; side constraint
UR - http://eudml.org/doc/104931
ER -

References

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  1. 1. R. E. CAMPELLO and N. MACULAN, A Lower Bound to the Set Partitioning Problem with Side Constraints, DRC-70-20-3, Design Research Center Report Series, Carnegie-Mellon University, Pittsburg, Pennylvania, 15213, U.S.A., 1983. 
  2. 2. K. DUDZINSKI and S. WALUKIEWICZ, Exact Methods for the Knapsack Problem and its Generalizations, European Journal of Operational Research (EJOR), Vol. 28, No. 1, 1987, pp. 3-21. Zbl0603.90097MR871368
  3. 3. M. E. DYER, A Geometric Approach to Two-Constraint Linear Programs with Generalized Upper Bounds, Advances in Computing Research, Vol. 1, 1983, pp. 79-90, JAI Press. 
  4. 4. M. E. DYER, An O (n) Algorithm for the Multiple-Choice Knapsack Linear Program, Mathematical Programming, Vol. 29, No. 1, 1984, pp. 57-63. Zbl0532.90068MR740505
  5. 5. E. L. JOHNSON and M. G. PADBERG, A Note on the Knapsack Problem with Special Ordered Sets, Operations Research Letters, Vol 1, No. 1, 1981, pp. 18-22. Zbl0493.90062MR643055
  6. 6. D. E. MULLER and F. P. PREPARATA, Finding the Intersection of Two Convex Polyhedra, Theoretical Computer Sciences, Vol. 7, 1978, pp. 217-238. Zbl0396.52002MR509019
  7. 7. R. T. ROCKAFELLAR, Convex Analysis, Princeton University Press, Princeton, N.J., U.S.A., 1970. Zbl0932.90001MR274683
  8. 8. E. ZEMEL, The Linear Multiple Choice Knapsack Problem, Operations Research, Vol. 28, No. 6, November-December, 1980, pp. 1412-1423. Zbl0447.90064MR609968

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