Approximating Bounded Degree Instances of NP-Hard Problems

We present some of the recent results on computational complexity of approximating bounded degree combinatorial optimization problems. In particular, we present the best up to now known explicit nonapproximability bounds on the very small degree optimization problems which are of particular importance on the intermediate stages of proving approximation hardness of some other generic optimization problems.

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

[2]  Sundar Vishwanathan,et al.  An Approximation Algorithm for the Asymmetric Travelling Salesman Problem with Distances One and Two , 1992, Inf. Process. Lett..

[3]  Carsten Lund,et al.  Proof verification and hardness of approximation problems , 1992, Proceedings., 33rd Annual Symposium on Foundations of Computer Science.

[4]  Sanjeev Arora,et al.  The Hardness of Approximate Optimia in Lattices, Codes, and Systems of Linear Equations , 1993, IEEE Annual Symposium on Foundations of Computer Science.

[5]  Mihalis Yannakakis,et al.  The Traveling Salesman Problem with Distances One and Two , 1993, Math. Oper. Res..

[6]  David P. Williamson,et al.  .879-approximation algorithms for MAX CUT and MAX 2SAT , 1994, STOC '94.

[7]  Piotr Berman,et al.  Approximating maximum independent set in bounded degree graphs , 1994, SODA '94.

[8]  Marek Karpinski,et al.  Polynomial time approximation schemes for dense instances of NP-hard problems , 1995, STOC '95.

[9]  Uriel Feige,et al.  Approximating the value of two power proof systems, with applications to MAX 2SAT and MAX DICUT , 1995, Proceedings Third Israel Symposium on the Theory of Computing and Systems.

[10]  Piotr Berman,et al.  On the Approximation Properties of Independent Set Problem in Degree 3 Graphs , 1999, WADS.

[11]  Vineet Bafna,et al.  Genome Rearrangements and Sorting by Reversals , 1996, SIAM J. Comput..

[12]  Dorit S. Hochbaum,et al.  Approximation Algorithms for NP-Hard Problems , 1996 .

[13]  Jacques Stern,et al.  The Hardness of Approximate Optima in Lattices, Codes, and Systems of Linear Equations , 1997, J. Comput. Syst. Sci..

[14]  M. Karpinski,et al.  Approximating dense cases of covering problems , 1996, Network Design: Connectivity and Facilities Location.

[15]  Johan Håstad,et al.  Some optimal inapproximability results , 1997, STOC '97.

[16]  Luca Trevisan,et al.  Constraint satisfaction: the approximability of minimization problems , 1997, Proceedings of Computational Complexity. Twelfth Annual IEEE Conference.

[17]  P. Berman,et al.  On Some Tighter Inapproximability Results , 1998, Electron. Colloquium Comput. Complex..

[18]  U. Feige.  A threshold of ln n for approximating set cover , 1998, JACM.

[19]  Guy Kindler,et al.  Approximating CVP to Within Almost-Polynomial Factors is NP-Hard , 2003, Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280).

[20]  Marek Karpinski,et al.  On the Approximation Hardness of Dense TSP and Other Path Problems , 1999, Inf. Process. Lett..

[21]  Marek Karpinski,et al.  On Some Tighter Inapproximability Results (Extended Abstract) , 1999, ICALP.

[22]  Alberto Caprara,et al.  Formulations and hardness of multiple sorting by reversals , 1999, RECOMB.

[23]  Robert Krauthgamer,et al.  A polylogarithmic approximation of the minimum bisection , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[24]  Johan Håstad,et al.  On bounded occurrence constraint satisfaction , 2000, Inf. Process. Lett..

[25]  Marek Karpinski,et al.  Approximation Algorithms for MAX-BISECTION on Low Degree Reg ular Graphs and Planar Graphs , 2000, Electron. Colloquium Comput. Complex..

[26]  Marek Karpinski,et al.  Approximation Hardness of TSP with Bounded Metrics , 2001, ICALP.

[27]  Marek Karpinski,et al.  Improved approximation of Max-Cut on graphs of bounded degree , 2002, J. Algorithms.

[28]  Marek Karpinski,et al.  A note on approximating Max-Bisection on regular graphs , 2001, Inf. Process. Lett..

[29]  Luca Trevisan,et al.  Non-approximability results for optimization problems on bounded degree instances , 2001, STOC '01.

[30]  A Unified Framework for Obtaining Improved Approximation Algorithms for Maximum Graph Bisection Problems , 2001, IPCO.

[31]  Klaus Jansen,et al.  Polynomial Time Approximation Schemes for MAX-BISECTION on Planar and Geometric Graphs , 2001, SIAM J. Comput..

[32]  Marek Karpinski,et al.  Approximation Hardness of Bounded Degree MIN-CSP and MIN-BISECTION , 2002, ICALP.

[33]  Johan Håstad,et al.  Some optimal inapproximability results , 2001, JACM.

[34]  P. Berman,et al.  Approximating Minimum Unsatissability of Linear Equations , 2001 .

[35]  Marek Karpinski,et al.  Polynomial Time Approximation Schemes for Some Dense Instances of NP-Hard Optimization Problems , 1997, Algorithmica.

[36]  Lars Engebretsen,et al.  An Explicit Lower Bound for TSP with Distances One and Two , 1999, Algorithmica.

[37]  Marek Karpinski,et al.  Approximating minimum unsatisfiability of linear equations , 2002, SODA '02.

[38]  Marek Karpinski,et al.  1.375-Approximation Algorithm for Sorting by Reversals , 2002, ESA.