### 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 language | English (US) |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Pages | 250-261 |

Number of pages | 12 |

Volume | 6213 LNCS |

DOIs | |

State | Published - 2010 |

Event | 4th International Frontiers of Algorithmics Workshop, FAW 2010 - Wuhan, China Duration: Aug 11 2010 → Aug 13 2010 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 6213 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 4th International Frontiers of Algorithmics Workshop, FAW 2010 |
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Country | China |

City | Wuhan |

Period | 8/11/10 → 8/13/10 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

^{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

**O((logn) ^{2}) time online approximation schemes for bin packing and subset sum problems.** / Ding, Liang; Fu, Bin; Fu, Yunhui; Lu, Zaixin; Zhao, Zhiyu.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

^{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, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6213 LNCS, pp. 250-261, 4th International Frontiers of Algorithmics Workshop, FAW 2010, Wuhan, China, 8/11/10. https://doi.org/10.1007/978-3-642-14553-7_24

^{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. 2010. p. 250-261. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-14553-7_24

}

TY - GEN

T1 - O((logn)2) time online approximation schemes for bin packing and subset sum problems

AU - Ding, Liang

AU - Fu, Bin

AU - Fu, Yunhui

AU - Lu, Zaixin

AU - Zhao, Zhiyu

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=77955864421&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77955864421&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-14553-7_24

DO - 10.1007/978-3-642-14553-7_24

M3 - Conference contribution

AN - SCOPUS:77955864421

SN - 3642145523

SN - 9783642145520

VL - 6213 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 250

EP - 261

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

ER -