Approximation Schemes for Geometric NP-Hard Problems: A Survey

Geometric optimization problems arise in many disciplines and are often NP- hard. One example is the famous Traveling Salesman Problem (TSP): given n points in the plane (more generally, in ℜd), find the shortest closed path that visits them all.

[1]  Joseph S. B. Mitchell,et al.  Guillotine Subdivisions Approximate Polygonal Subdivisions: A Simple Polynomial-Time Approximation Scheme for Geometric TSP, k-MST, and Related Problems , 1999, SIAM J. Comput..

[2]  Gerhard J. Woeginger,et al.  The Maximum Traveling Salesman Problem Under Polyhedral Norms , 1998, IPCO.

[3]  Claire Mathieu,et al.  A Randomized Approximation Scheme for Metric MAX-CUT , 1998, FOCS.

[4]  Satish Rao,et al.  Approximating geometrical graphs via “spanners” and “banyans” , 1998, STOC '98.

[5]  Sanjeev Arora,et al.  Approximation schemes for minimum latency problems , 1999, STOC '99.

[6]  D. Eppstein,et al.  Approximation algorithms for geometric problems , 1996 .

[7]  Tetsuo Asano,et al.  Covering points in the plane by k-tours: towards a polynomial time approximation scheme for general k , 1997, STOC '97.

[8]  Satish Rao,et al.  Approximation schemes for Euclidean k-medians and related problems , 1998, STOC '98.

[9]  Sanjeev Arora,et al.  Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems , 1998, JACM.

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

[11]  Satish Rao,et al.  A Nearly Linear-Time Approximation Scheme for the Euclidean kappa-median Problem , 1999, ESA.

[12]  Eugene L. Lawler,et al.  Traveling Salesman Problem , 2016 .

[13]  Sanjeev Arora,et al.  Polynomial time approximation schemes for Euclidean TSP and other geometric problems , 1996, Proceedings of 37th Conference on Foundations of Computer Science.

[14]  Andrzej Lingas,et al.  A Polynomial Time Approximation Scheme for Euclidean Minimum Cost k-Connectivity , 1998, ICALP.