The hardness of approximation: Gap location

The author refines the complexity analysis of approximation problems, by relating it to a new parameter called gap location. Many of the results obtained so far for approximations yield satisfactory analysis also with respect to this refined parameter, but some known results (e.g. max-k-colorability, max-3-dimensional matching and max not-all-equal 3sat) fall short of doing so. A second contribution of is in filling the gap in these cases by presenting new reductions. Next, he presents definitions and hardness results of new approximation versions of some NP-complete optimization problems. The problems are: vertex cover, k-edge coloring, set splitting, and a restricted version of feedback vertex set and feedback arc set.<<ETX>>

[1]  Zvi Galil,et al.  Explicit Constructions of Linear-Sized Superconcentrators , 1981, J. Comput. Syst. Sci..

[2]  Carsten Lund,et al.  On the hardness of approximating minimization problems , 1993, STOC.

[3]  Vojtech Rödl,et al.  The algorithmic aspects of the regularity lemma , 1992, Proceedings., 33rd Annual Symposium on Foundations of Computer Science.

[4]  Marshall W. Bern,et al.  The Steiner Problem with Edge Lengths 1 and 2 , 1989, Inf. Process. Lett..

[5]  Carsten Lund,et al.  Proof verification and the intractability of approximation problems , 1992, FOCS 1992.

[6]  Miklós Ajtai,et al.  Recursive construction for 3-regular expanders , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[7]  Sanjeev Arora,et al.  Probabilistic checking of proofs; a new characterization of NP , 1992, Proceedings., 33rd Annual Symposium on Foundations of Computer Science.

[8]  David S. Johnson,et al.  Computers and In stractability: A Guide to the Theory of NP-Completeness. W. H Freeman, San Fran , 1979 .

[9]  Mihalis Yannakakis,et al.  Optimization, approximation, and complexity classes , 1991, STOC '88.

[10]  László Lovász,et al.  Approximating clique is almost NP-complete , 1991, [1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science.

[11]  Claude Berge,et al.  Graphs and Hypergraphs , 2021, Clustering.

[12]  Teofilo F. Gonzalez,et al.  P-Complete Approximation Problems , 1976, J. ACM.

[13]  David S. Johnson,et al.  The Complexity of Near-Optimal Graph Coloring , 1976, J. ACM.

[14]  Zvi Galil,et al.  NP Completeness of Finding the Chromatic Index of Regular Graphs , 1983, J. Algorithms.