### Abstract

A wide variety of approximation algorithms for permanents of non-negative matrices has been proposed and analyzed before [5; 7; 9; 1]. Usually, these approximation algorithms have been presented for 0-1 matrices and it has been remarked that they extend to other matrices as long as all entries are non-negative. Here we present the first approximation algorithm for the permanent of an arbitrary complex matrix. We extend the notion of an (ε,δ)-approximation algorithm to accommodate for cancellations in additions. Our running time is Õ(3^{n/2} ε^{-2} log 1/δ) compared to Õ(2^{n/2} ε^{-2} log 1/δ) for non-negative matrices. (A faster algorithm is known for 0-1 matrices [6].).

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

Pages | 667-669 |

Number of pages | 3 |

DOIs | |

State | 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 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Software

### Cite this

*Proceedings of the 32nd Annual ACM Symposium on Theory of Computing, STOC 2000*(pp. 667-669). (Proceedings of the Annual ACM Symposium on Theory of Computing). https://doi.org/10.1145/335305.335399

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*Proceedings of the 32nd Annual ACM Symposium on Theory of Computing, STOC 2000.*Proceedings of the Annual ACM Symposium on Theory of Computing, pp. 667-669, 32nd Annual ACM Symposium on Theory of Computing, STOC 2000, Portland, OR, United States, 5/21/00. https://doi.org/10.1145/335305.335399

**Approximating permanents of complex matrices.** / Furer, Martin.

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

TY - GEN

T1 - Approximating permanents of complex matrices

AU - Furer, Martin

PY - 2000/12/1

Y1 - 2000/12/1

N2 - A wide variety of approximation algorithms for permanents of non-negative matrices has been proposed and analyzed before [5; 7; 9; 1]. Usually, these approximation algorithms have been presented for 0-1 matrices and it has been remarked that they extend to other matrices as long as all entries are non-negative. Here we present the first approximation algorithm for the permanent of an arbitrary complex matrix. We extend the notion of an (ε,δ)-approximation algorithm to accommodate for cancellations in additions. Our running time is Õ(3n/2 ε-2 log 1/δ) compared to Õ(2n/2 ε-2 log 1/δ) for non-negative matrices. (A faster algorithm is known for 0-1 matrices [6].).

AB - A wide variety of approximation algorithms for permanents of non-negative matrices has been proposed and analyzed before [5; 7; 9; 1]. Usually, these approximation algorithms have been presented for 0-1 matrices and it has been remarked that they extend to other matrices as long as all entries are non-negative. Here we present the first approximation algorithm for the permanent of an arbitrary complex matrix. We extend the notion of an (ε,δ)-approximation algorithm to accommodate for cancellations in additions. Our running time is Õ(3n/2 ε-2 log 1/δ) compared to Õ(2n/2 ε-2 log 1/δ) for non-negative matrices. (A faster algorithm is known for 0-1 matrices [6].).

UR - http://www.scopus.com/inward/record.url?scp=0033717560&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033717560&partnerID=8YFLogxK

U2 - 10.1145/335305.335399

DO - 10.1145/335305.335399

M3 - Conference contribution

SN - 1581131844

SN - 9781581131840

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 667

EP - 669

BT - Proceedings of the 32nd Annual ACM Symposium on Theory of Computing, STOC 2000

ER -