Volume 50, Number 4-5, October-December 2016
|Page(s)||995 - 1001|
|Published online||03 November 2016|
An improved binary search algorithm for the Multiple-Choice Knapsack Problem∗
1 School of Science, Henan University of Technology, Zhengzhou,
Henan 450001, P.R. China.
2 Department of Computer Science, New Jersey Institute of Technology, Newark NJ - 07102, USA.
3 Department of Business and Economics, York College, The City University of New York, 94-20 Guy R. Brewer Blvd, Jamaica, New York 11451, USA.
4 Department of Information, Operations and Management Sciences, Stern School of Business, New York University, 44 West 4th Street, New York 10012-1126, USA.
Accepted: 24 September 2015
The Multiple-Choice Knapsack Problem is defined as a 0-1 Knapsack Problem with additional disjoint multiple-choice constraints. Gens and Levner presented for this problem an approximate binary search algorithm with a worst case ratio of 5. We present an improved approximate binary search algorithm with a ratio of 3 + (1/2)t and a running time O(n(t + log m)), where n is the number of items, m the number of classes, and t a positive integer. We then extend our algorithm to make it also applicable to the Multiple-Choice Multidimensional Knapsack Problem with dimension d.
Mathematics Subject Classification: 68Q25 / 90C10 / 90C27
Key words: Multiple-Choice Knapsack Problem (MCKP) / Approximate binary search algorithm / Worst-case performance ratio / Multiple-choice Multi-dimensional Knapsack Problem (MMKP)
© EDP Sciences, ROADEF, SMAI 2016
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