Constant-Time approximation algorithms for the knapsack problem

Authors:
Hiro Ito;Susumu Kiyoshima;Yuichi Yoshida
Affiliations:
School of Informatics, Kyoto University, Kyoto, Japan;School of Informatics, Kyoto University, Kyoto, Japan;School of Informatics, Kyoto University, Kyoto, Japan,Preferred Infrastructure, Inc., Tokyo, Japan
Venue:
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
Year:
2012

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Abstract

In this paper, we give a constant-time approximation algorithm for the knapsack problem. Using weighted sampling, with which we can sample items with probability proportional to their profits, our algorithm runs with query complexity O (ε −4 logε −1), and it approximates the optimal profit with probability at least 2/3 up to error at most an ε -fraction of the total profit. For the subset sum problem, which is a special case of the knapsack problem, we can improve the query complexity to O (ε −1 logε −1).