### Abstract

The Hamming center problem for a set S of k binary strings, each of length n, is to find a binary string β of length n that minimizes the maximum Hamming distance between β and any string in S. Its decision version is known to be NP-complete. We provide several approximation algorithms for the Hamming center problem. Our main result is a randomized (4/3+ε) approximation algorithm running in polynomial time if the Hamming radius of S is at least superlogarithmic in k. Furthermore, we show how to find in polynomial time a set B of O(log k) strings of length n such that for each string in S there is at least one string in B within Hamming distance not exceeding the radius of S.

Original language | English (US) |
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Pages | S905-S906 |

State | Published - Jan 1 1999 |

Externally published | Yes |

Event | Proceedings of the 1999 10th Annual ACM-SIAM Symposium on Discrete Algorithms - Baltimore, MD, USA Duration: Jan 17 1999 → Jan 19 1999 |

### Conference

Conference | Proceedings of the 1999 10th Annual ACM-SIAM Symposium on Discrete Algorithms |
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City | Baltimore, MD, USA |

Period | 1/17/99 → 1/19/99 |

### ASJC Scopus subject areas

- Software
- Mathematics(all)

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## Cite this

*Efficient approximation algorithms for the Hamming center problem*. S905-S906. Paper presented at Proceedings of the 1999 10th Annual ACM-SIAM Symposium on Discrete Algorithms, Baltimore, MD, USA, .