### Abstract

In this paper we present a theoretical analysis of the deterministic on-line Sum of Squares algorithm (SS) for bin packing, introduced and studied experimentally in [8], along with several new variants. SS is applicable to any instance of bin packing in which the bin capacity B and item sizes s(a) are integral (or can be scaled to be so), and runs in time O(nB). It performs remarkably well from an average case point of view: For any discrete distribution in which the optimal expected waste is sublinear, SS also has sublinear expected waste. For any discrete distribution where the optimal expected waste is bounded, SS has expected waste at most O(log n). In addition, we present a randomized O(nB log B)-time on-line algorithm SS*, based on SS, whose expected behavior is essentially optimal for all discrete distributions. Algorithm SS* also depends on a new linear-programming- based pseudopolynomial-time algorithm for solving the NP-hard problem of determining, given a discrete distribution F, just what is the growth rate for the optimal expected waste. An off-line randomized variant SS** performs well in a worst-case sense: For any list L of integer-sized items to be packed into bins of a fixed size B, the expected number of bins used by SS** is at most OPT(L) + √OPT(L).

Original language | English |
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Title of host publication | Proceedings of the 32nd Annual ACM Symposium on Theory of Computing, STOC 2000 |

Pages | 208-217 |

Number of pages | 10 |

DOIs | |

Publication status | Published - Dec 1 2000 |

Event | 32nd Annual ACM Symposium on Theory of Computing, STOC 2000 - Portland, OR, United States Duration: May 21 2000 → May 23 2000 |

### Publication series

Name | Proceedings of the Annual ACM Symposium on Theory of Computing |
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ISSN (Print) | 0737-8017 |

### Conference

Conference | 32nd Annual ACM Symposium on Theory of Computing, STOC 2000 |
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Country | United States |

City | Portland, OR |

Period | 5/21/00 → 5/23/00 |

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### ASJC Scopus subject areas

- Software

### Cite this

*Proceedings of the 32nd Annual ACM Symposium on Theory of Computing, STOC 2000*(pp. 208-217). (Proceedings of the Annual ACM Symposium on Theory of Computing). https://doi.org/10.1145/335305.335331