### 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 | Frontiers in Algorithmics - 4th International Workshop, FAW 2010, Proceedings |

Pages | 250-261 |

Number of pages | 12 |

DOIs | |

State | Published - Aug 27 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) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### 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 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

^{2}) time online approximation schemes for bin packing and subset sum problems. In

*Frontiers in Algorithmics - 4th International Workshop, FAW 2010, Proceedings*(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