## Abstract

The search version for NP-complete combinatorial optimization problems asks for finding a solution of optimal value. Such a solution is called a witness. We follow a recent paper by Kumar and Sivakumar, and study a relatively new notion of approximate solutions that ignores the value of a solution and instead considers its syntactic representation (under some standard encoding scheme). The results that we present are of a negative nature. We show that for many of the well known NP-complete problems (such as 3-SAT, CLIQUE, 3-COLORING, SET COVER) it is NP-hard to produce a solution whose Hamming distance from an optimal solution is substantially closer than what one would obtain by just taking a random solution. In fact, we have been able to show similar results for most of Karp’s 21 original NP-complete problems. (At the moment, our results are not tight only for UNDIRECTED HAMILTONIAN CYCLE and FEEDBACK EDGE SET).

Original language | English |
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Title of host publication | Approximation Algorithms for Combinatorial Optimization - 3rd International Workshop, APPROX 2000, Proceedings |

Editors | Klaus Jansen, Samir Khuller |

Publisher | Springer Verlag |

Pages | 120-131 |

Number of pages | 12 |

ISBN (Electronic) | 9783540679967 |

DOIs | |

State | Published - 2000 |

Externally published | Yes |

Event | 3rd International Workshop on Approximation Algorithms for Combinatorial Optimization, APPROX 2000 - Saarbrucken, Germany Duration: 5 Sep 2000 → 8 Sep 2000 |

### 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 | 1913 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 3rd International Workshop on Approximation Algorithms for Combinatorial Optimization, APPROX 2000 |
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Country/Territory | Germany |

City | Saarbrucken |

Period | 5/09/00 → 8/09/00 |

### Bibliographical note

Publisher Copyright:© Springer-Verlag Berlin Heidelberg 2000.