Minimum length corridor problem on grids

Publication Date

7-1-2025

Document Type

Article

Publication Title

Involve

Volume

18

Issue

4

DOI

10.2140/involve.2025.18.665

First Page

665

Last Page

682

Abstract

Let B be a rectangle that is decomposed into subrectangles. A corridor of B is a tree T whose edges belong to B, where T has a vertex in the outer boundary and in each of the subrectangles in B. A minimum-length corridor (MLC) is a corridor with the smallest length sum over its edges. In this paper, we determine the minimum-length corridor of the rectangles that are subdivided by horizontal and vertical lines into smaller rectangles (grids) when all horizontal (or vertical) line segments have the same length k and the rest of the line segments have a length of at least k. We also determine an upper bound for the minimum-length corridor of the grids when all horizontal (or vertical) line segments have the same length k and the rest of line segments have length at most k. We conclude with a conjecture that the upper bound is tight for some cases.

Funding Number

CMMI-1727743

Funding Sponsor

National Science Foundation

Keywords

applications of graph theory, geometric aspects of graph theory, tiling, trees

Department

Mathematics and Statistics

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