A NOTE ON DUAL APPROXIMATION ALGORITHMS FOR CLASS CONSTRAINED BIN PACKING PROBLEMS

Author(s)

Xavier, Eduardo C. ^[1] ; Miyazawa, Flavio Keidi ^[1]

Affiliation

^[1] Univ Estadual Campinas, UNICAMP, Inst Comp, BR-13083970 Campinas, SP - Brazil

• Document type: Journal article
• Source: RAIRO-THEORETICAL INFORMATICS AND APPLICATIONS; v. 43, n. 2, p. 239-248, APR-JUN 2009.
• Web of Science Citations: 1

Abstract

In this paper we present a dual approximation scheme for the class constrained shelf bin packing problem. In this problem, we are given bins of capacity 1, and n items of Q different classes, each item e with class c(e) and size s(e). The problem is to pack the items into bins, such that two items of different classes packed in a same bin must be in different shelves. Items in a same shelf are packed consecutively. Moreover, items in consecutive shelves must be separated by shelf divisors of size d. In a shelf bin packing problem, we have to obtain a shelf packing such that the total size of items and shelf divisors in any bin is at most 1. A dual approximation scheme must obtain a shelf packing of all items into N bins, such that, the total size of all items and shelf divisors packed in any bin is at most 1 + epsilon for a given epsilon > 0 and N is the number of bins used in an optimum shelf bin packing problem. Shelf divisors are used to avoid contact between items of different classes and can hold a set of items until a maximum given weight. We also present a dual approximation scheme for the class constrained bin packing problem. In this problem, there is no use of shelf divisors, but each bin uses at most C different classes. (AU)

• FAPESP's process: 08/01490-3 - Algorithms for packing and graph problems
• Grantee: Eduardo Candido Xavier
• Support Opportunities: Regular Research Grants