O((logn)2) time online approximation schemes for bin packing and subset sum problems

Liang Ding, Bin Fu, Yunhui Fu, Zaixin Lu, Zhiyu Zhao

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Given a set S = {b 1,⋯, b n } of integers and an integer s, the subset sum problem is to decide if there is a subset S′ of S such that the sum of elements in S′ is exactly equal to s. We present an online approximation scheme for this problem. It updates in O(logn) time and gives a (1+ε)-approximation solution in time. The online approximation for target s is to find a subset of the items that have been received. The bin packing problem is to find the minimum number of bins of size one to pack a list of items a 1,⋯, a n of size in [0,1]. Let function bp(L) be the minimum number of bins to pack all items in the list L. We present an online approximate algorithm for the function bp(L) in the bin packing problem, where L is the list of the items that have been received. It updates in O(logn) updating time and gives a (1+ε)-approximation solution app(L) for bp(L) in time to satisfy app(L)≤(1+ε)bp(L)+1.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages250-261
Number of pages12
Volume6213 LNCS
DOIs
Publication statusPublished - 2010
Event4th International Frontiers of Algorithmics Workshop, FAW 2010 - Wuhan, China
Duration: Aug 11 2010Aug 13 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6213 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other4th International Frontiers of Algorithmics Workshop, FAW 2010
CountryChina
CityWuhan
Period8/11/108/13/10

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ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Ding, L., Fu, B., Fu, Y., Lu, Z., & Zhao, Z. (2010). O((logn)2) time online approximation schemes for bin packing and subset sum problems. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6213 LNCS, pp. 250-261). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6213 LNCS). https://doi.org/10.1007/978-3-642-14553-7_24