Removable online knapsack problems

Abstract

We introduce an on-line model for a class of hand-making games such as Rummy and Mah-Jang. An input is a sequence of items, u1,⋯, ui, ⋯ such that 0 < |ui| ≤1.0. When ui is given, the on-line player puts it into the bin and can discard any selected items currently in the bin (including ui) under the condition that the total size of the remaining items is at most one. The goal is to make this total size as close to 1.0 as possible when the game ends. We also discuss the multibin model, where the player can select a bin out of the κ ones which ui is put into. We prove tight bounds for the competitive ratio of this problem, both for κ = 1 and κ ≥ 2. © 2002 Springer-Verlag Berlin Heidelberg.