### Abstract

Given a k-uniform hyper-graph, the Ek-Vertex-Cover problem is to find the smallest subset of vertices that intersects every hyper-edge. We present a new multilayered PCP construction that extends the Raz verifier. This enables us to prove that Ek-Vertex-Cover is NP-hard to approximate within factor (k -1 - ε) for any k ≥ 3 and any ε > 0. The result is essentially tight as this problem can be easily approximated within factor k. Our construction makes use of the biased Long-Code and is analyzed using combinatorial properties of s-wise t-intersecting families of subsets.

Original language | English (US) |
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Title of host publication | Conference Proceedings of the Annual ACM Symposium on Theory of Computing |

Pages | 595-601 |

Number of pages | 7 |

State | Published - 2003 |

Event | 35th Annual ACM Symposium on Theory of Computing - San Diego, CA, United States Duration: Jun 9 2003 → Jun 11 2003 |

### Other

Other | 35th Annual ACM Symposium on Theory of Computing |
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Country | United States |

City | San Diego, CA |

Period | 6/9/03 → 6/11/03 |

### Fingerprint

### Keywords

- Hardness of Approximation
- Hypergraph Vertex Cover
- Long Code
- Multilayered PCP

### ASJC Scopus subject areas

- Software

### Cite this

*Conference Proceedings of the Annual ACM Symposium on Theory of Computing*(pp. 595-601)

**A new multilayered PCP and the hardness of hypergraph vertex cover.** / Dinur, Irit; Khot, Subhash; Guruswami, Venkatesan; Regev, Oded.

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

*Conference Proceedings of the Annual ACM Symposium on Theory of Computing.*pp. 595-601, 35th Annual ACM Symposium on Theory of Computing, San Diego, CA, United States, 6/9/03.

}

TY - GEN

T1 - A new multilayered PCP and the hardness of hypergraph vertex cover

AU - Dinur, Irit

AU - Khot, Subhash

AU - Guruswami, Venkatesan

AU - Regev, Oded

PY - 2003

Y1 - 2003

N2 - Given a k-uniform hyper-graph, the Ek-Vertex-Cover problem is to find the smallest subset of vertices that intersects every hyper-edge. We present a new multilayered PCP construction that extends the Raz verifier. This enables us to prove that Ek-Vertex-Cover is NP-hard to approximate within factor (k -1 - ε) for any k ≥ 3 and any ε > 0. The result is essentially tight as this problem can be easily approximated within factor k. Our construction makes use of the biased Long-Code and is analyzed using combinatorial properties of s-wise t-intersecting families of subsets.

AB - Given a k-uniform hyper-graph, the Ek-Vertex-Cover problem is to find the smallest subset of vertices that intersects every hyper-edge. We present a new multilayered PCP construction that extends the Raz verifier. This enables us to prove that Ek-Vertex-Cover is NP-hard to approximate within factor (k -1 - ε) for any k ≥ 3 and any ε > 0. The result is essentially tight as this problem can be easily approximated within factor k. Our construction makes use of the biased Long-Code and is analyzed using combinatorial properties of s-wise t-intersecting families of subsets.

KW - Hardness of Approximation

KW - Hypergraph Vertex Cover

KW - Long Code

KW - Multilayered PCP

UR - http://www.scopus.com/inward/record.url?scp=0038107530&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0038107530&partnerID=8YFLogxK

M3 - Conference contribution

SP - 595

EP - 601

BT - Conference Proceedings of the Annual ACM Symposium on Theory of Computing

ER -