We study the Minimum-Length Corridor (MLC) problem. Given a rectangular boundary partitioned into rectilinear polygons, the objective is to find a corridor of least total length. A corridor is a set of line segments each of which must lie along the line segments that form the rectangular boundary and/or the boundary of the rectilinear polygons. The corridor is a tree, and must include at least one point from the rectangular boundary and at least one point from the boundary of each of the rectilinear polygons. We establish the NP-completeness of the decision version of the MLC problem even when it is restricted to a rectangular boundary partitioned into rectangles.
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 MLC
k
problems. The MLC
k
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 MLC
k
problem. Our algorithms are based on the restriction and relaxation approximation techniques.
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