Guillotine Subdivisions Approximate Polygonal Subdivisions: A Simple Polynomial-Time Approximation Scheme for Geometric TSP, k -MST, and Related Problems
Joseph S. B. Mitchell · SIAM Journal on Computing · 1999
We show that any polygonal subdivision in the plane can be converted into an "m-guillotine" subdivision whose length is at most $(1+{c\over m})$ times that of the original subdivision, for a small constant c. "m-Guillotine" subdivisions have a simple recursive structure that allows one to search for the shortest of such subdivisions in polynomial time, using dynamic programming. In particular, a consequence of our main theorem is a simple polynomial-time approximation scheme for geometric instances of several network optimization problems, including the Steiner minimum spanning tree, the traveling salesperson problem (TSP), and the k-MST problem.