Indexed by:Journal Papers

Date of Publication:2019-09-27

Journal:THEORETICAL COMPUTER SCIENCE

Included Journals:EI、SCIE

Volume:786

Page Number:88-95

ISSN:0304-3975

Key Words:Online algorithms; Knapsack problems; Competitive ratio

Abstract:In this paper, we address an online knapsack problem under concave function f(x), i.e., an item with size x has its profit f (x). We first obtain a simple lower bound max{q, f'(0)/f(1)}, where holden ratio q approximate to 1.618, then show that this bound is not tight, and give an improved lower bound. Finally, we find the online algorithm for linear function can be employed to the concave case, and prove its competitive ratio is f'(0)/f(1/q), then we give a refined online algorithm with a competitive ratio f'(0)/f(1) + 1 when f'(0)/f(1) is very large. And we also give optimal algorithms for some specific piecewise linear functions. (C) 2018 Elsevier B.V. All rights reserved.