An improved binary search algorithm for the Multiple-Choice Knapsack Problem

Authors

Cheng He, Henan University of Technology
Joseph Y.T. Leung, Department of Computer Science
Kangbok Lee, York College CUNY
Michael L. Pinedo, Leonard N. Stern School of Business

Document Type

Article

Publication Date

10-1-2016

Abstract

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 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.

Identifier

84994607447 (Scopus)

Publication Title

RAIRO Operations Research

External Full Text Location

https://doi.org/10.1051/ro/2015061

e-ISSN

28047303

First Page

995

Last Page

1001

Issue

4-5

Volume

50

Recommended Citation

He, Cheng; Leung, Joseph Y.T.; Lee, Kangbok; and Pinedo, Michael L., "An improved binary search algorithm for the Multiple-Choice Knapsack Problem" (2016). Faculty Publications. 10259.
https://digitalcommons.njit.edu/fac_pubs/10259