Restricted parameter range promise set cover problems are easy

Hao CHEN

Front. Math. China ›› 2014, Vol. 9 ›› Issue (6) : 1253 -1260.

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Front. Math. China ›› 2014, Vol. 9 ›› Issue (6) : 1253 -1260. DOI: 10.1007/s11464-014-0429-8
RESEARCH ARTICLE
RESEARCH ARTICLE

Restricted parameter range promise set cover problems are easy

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Abstract

The restricted parameter range set cover problem is a weak form of the NP-hard set cover problem with the restricted range of parameters. We give a polynomial time algorithm for this problem by lattices.

Keywords

Set cover problem / lattice / closest vector problem (CVP) / shortest vector problem (SVP)

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Hao CHEN. Restricted parameter range promise set cover problems are easy. Front. Math. China, 2014, 9(6): 1253-1260 DOI:10.1007/s11464-014-0429-8

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References

[1]

Ajtai M. The shortest vector problem in L2 is NP-hard for randomized reductions (extended abstract). In: Proc STOC 1998. 1998, 10−19

[2]

Arora S, Babai L, Stern J, Sweedyk Z. The hardness of approximating optima in lattices, codes and systems of linear equations. J Comput System Sci, 1997, 54(2): 317−331

[3]

Bansal N, Khot S. Inapproximability of hypergraph vertex cover and applications to scheduling problems. Preprint, 2009

[4]

Bellare M, Goldwasser S, Lund C, Russell A. Efficient multi-prover interactive proofs with applications to approximation problems. In: Proc STOC 1993. 1993, 113−131

[5]

Chvatal V. A greedy heuristic for the set-covering problem. Math Oper Res, 1979, 4: 233−235

[6]

Dinur I, Guruswami V, Khot S, Regev O. A new multilayered PCP and the hardness of hypergraph vertex cover. SIAM J Comput, 2005, 34(5): 1129−1146

[7]

Dinur I, Kindler G, Raz R, Safra S. An improved lower bound for approximating CVP. Combinatorica, 2003, 23(2): 205−243

[8]

Dumer I, Micciancio D, Sudan M. Hardness of approximating the minimum distance of a linear code. IEEE Trans Inform Theory, 2003, 49(1): 22−37

[9]

Feige U. A threshold of ln n for approximating set cover. J ACM, 1998, 45(4): 634−652

[10]

Haviv I, Regev O. Tensor-based hardness of the shortest vector problem to within almost polynomial factors. In: Proc STOC 2007. 2007, 469−477

[11]

Hochbaum D. Approximation algorithms for set covering and vertex cover problems. SIAM J Comput, 1982, 11: 555−556

[12]

Johnson D S. Approximation algorithms for combinatorial problems. J Comput System Sci, 1974, 9: 256−278

[13]

Khot S. Hardness of approximating the shortest vector problem in lattices. J ACM, 2005, 52(5): 789−808

[14]

Khot S, Regev O. Vertex cover might be hard to approximate to within 2−ε. In: Proc 18th IEEE Annual Conference on Computational Complexity. Los Alamitos: IEEE Computer Society Press, 2003, 379−386

[15]

Lovasz L. On the ratio of optimal integral and fractional covers. Discrete Math, 1975, 13: 383−390

[16]

Lund C, Yannakakis M. Hardness of approximating minimization problem. J ACM, 1994, 41(5): 960−981

[17]

Micciancio D. The shortest vector problem is NP-hard to approximate within some constant. SIAM J Comput, 2001, 30(6): 2008−2035

[18]

Micciancio D, Goldwasser S. Complexity of Lattice Problems: A Cryptographic Perspective. Dordrecht: Kluwer Academic Publishers, 2002

[19]

Raz R, Safra S. A sub-constant error-probability low degree test and a sub-constant error-probability PCP characteristic of NP. In: Proc STOC 1997. 1997, 475−484

[20]

Trevisan L. Non-approximability results for optimization problems on bounded degree instances. In: Proc STOC 2001. 2001, 453−461

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