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by Lars Engebretsen, Jonas Holmerin
In Proceedings of the 18th IEEE Conference on Computational Complexity
http://www.nada.kth.se/~enge/papers/3Q-PCP.pdf
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Abstract:
Abstract. We study non-Boolean PCPs that have perfect completeness and read three positions from the proof. For the case when the proof consists of values from a domain of size d for some integer constant d ≥ 2, we construct a non-adaptive PCP with perfect completeness and soundness d −1 +d −2 +ε, for any constant ε> 0, and an adaptive PCP with perfect completeness and soundness d −1 + ε, for any constant ε> 0. These results match the best known constructions for the case d = 2 and our proofs also show that the particular predicates we use in our PCPs are non-approximable beyond the random assignment threshold. 1
Citations
|
426
|
Some optimal inapproximability results
– Hastad
- 1997
|
|
393
|
A Threshold of ln n for Approximating Set Cover
– Feige
- 1998
|
|
198
|
A parallel repetition theorem
– Raz
- 1998
|
|
52
|
Approximation algorithms for constraint satisfaction problems involving at most three variables per constraint
– Zwick
- 1998
|
|
47
|
Fourier analysis on finite groups and applications
– Terras
- 1999
|
|
46
|
Proof Veri and Hardness of Approximation Problems
– Arora, Lund, et al.
- 1998
|
|
42
|
A PCP characterization of NP with optimal amortized query complexity
– Samorodnitsky, Trevisan
- 2000
|
|
30
|
Hardness of approximate hypergraph coloring
– Guruswami, Hastad, et al.
- 2000
|
|
28
|
A tight characterization of NP with 3 query PCPs
– Guruswami, Lewin, et al.
- 1998
|
|
13
|
Parallel approximation algorithms by positive linear programming
– Trevisan
- 1998
|
|
11
|
Vertex cover on 4-regular hyper-graphs is hard to approximate within 2
– Holmerin
- 2002
|
|
11
|
Rajeev Motwani, Madhu Sudan, and Márió Szegedy. Proof verification and the hardness of approximation problems
– Arora, Lund
- 1998
|
|
7
|
The non-approximability of non-Boolean predicates
– Engebretsen
- 2001
|
|
7
|
Improved inapproximability results for vertex cover on k-uniform hypergraphs
– Holmerin
- 2002
|
|
7
|
Hardness results for approximate hypergraph coloring
– Khot
- 2002
|
|
7
|
Query efficient PCPs with perfect completeness
– Hastad, Khot
- 2001
|
|
3
|
Hardness of coloring 3-uniform hypergraphs and hardness of the not-all-equal predicate
– Khot
- 2002
|
|
3
|
Fatos Xhafa. The (parallel) approximability of non-Boolean satisability problems and restricted integer programming
– Serna, Trevisan
- 1998
|
|
2
|
Approximating satisfiable satsifiabiliy problems
– Trevisan
- 2000
|
|
1
|
Query ecient PCPs with perfect completeness
– Hastad, Khot
- 2001
|
|
1
|
Approximating satis satsi problems. Algorithmica
– Trevisan
- 2000
|
