A Tale on Guillotine Cut

The guillotine cut is an important tool to design polynomial- time approximation schemes for geometric optimization problems. In this article, we survey its history and recent developments.

[1]  Christos Levcopoulos.  Fast heuristics for minimum length rectangular partitions of polygons , 1986, SCG '86.

[2]  Bing Lu,et al.  A Polynomial Time Approximation Scheme for the Problem of Interconnecting Highways , 2001, J. Comb. Optim..

[3]  Bing Lu,et al.  Polynomial Time Approximation Scheme for the Rectilinear Steiner Arborescence Problem , 2000, J. Comb. Optim..

[4]  Andrzej Lingas.  Heuristics for minimum edge length rectangular partitions of rectilinear figures , 1983, Theoretical Computer Science.

[5]  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..

[6]  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.

[7]  Joseph S. B. Mitchell,et al.  Guillotine subdivisions approximate polygonal subdivisions: a simple new method for the geometric k-MST problem , 1996, SODA '96.

[8]  Ding-Zhu Du,et al.  On heuristics for minimum length rectilinear partitions , 2005, Algorithmica.

[9]  Santosh S. Vempala,et al.  A Constant-Factor Approximation Algorithm for the Geometric k-MST Problem in the Plane , 1999, SIAM J. Comput..

[10]  Andrzej Lingas.  Heuristics for minimum edge length rectangular partitions of rectilinear figures , 1983 .

[11]  Sanjeev Arora,et al.  Nearly Linear Time Approximation Schemes for Euclidean TSP and Other Geometric Problems , 1997, RANDOM.

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

[13]  Man-Tak Shing,et al.  On optimal routing trees , 1988 .

[14]  Teofilo F. Gonzalez,et al.  Bounds for partitioning rectilinear polygons , 1985, SCG '85.

[15]  Teofilo F. Gonzalez,et al.  Inproved Bounds for Rectangular and Guillotine Partitions , 1989, J. Symb. Comput..

[16]  Xiaohua Jia,et al.  A Polynomial Time Approximation Scheme for the Grade of Service Steiner Minimum Tree Problem , 2002, J. Glob. Optim..

[17]  Bing Lu,et al.  Polynomial Time Approximation Scheme for Symmetric Rectilinear Steiner Arborescence Problem , 2001, J. Glob. Optim..