Approximating corridors and tours via restriction and relaxation techniques

Given a rectangular boundary partitioned into rectangles, the Minimum-Length Corridor (MLC-R) problem consists of finding a corridor of least total length. A corridor is a set of connected line segments, each of which must lie along the line segments that form the rectangular boundary and/or the boundary of the rectangles, and must include at least one point from the boundary of every rectangle and from the rectangular boundary. The MLC-R problem is known to be NP-hard. We present the first polynomial-time constant ratio approximation algorithm for the MLC-R and MLCk problems. The MLCk problem is a generalization of the MLC-R problem where the rectangles are rectilinear c-gons, for c ≤ k and k is a constant. We also present the first polynomial-time constant ratio approximation algorithm for the Group Traveling Salesperson Problem (GTSP) for a rectangular boundary partitioned into rectilinear c-gons as in the MLCk problem. Our algorithms are based on the restriction and relaxation...

• Type: Journal
• Year: 2010
• Where: TALG
• Authors: Arturo Gonzalez-Gutierrez, Teofilo F. Gonzalez
• Keywords: Algorithms, Mlck Problem, Rectangular Boundary, TALG 2010