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Minimum length corridor problem on grids

Sogol Jahanbekam, Sindhu Ramu and Elham Sohrabi

Vol. 18 (2025), No. 4, 665–682
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.

Keywords
trees, geometric aspects of graph theory, applications of graph theory, tiling
Mathematical Subject Classification
Primary: 05B45, 05C05, 05C09, 05C90
Milestones
Received: 7 September 2023
Revised: 28 February 2024
Accepted: 6 March 2024
Published: 30 July 2025

Communicated by Joshua Cooper
Authors
Sogol Jahanbekam
Department of Mathematics and Statistics
San Jose State University
San Jose, CA
United States
Sindhu Ramu
Department of Mathematics and Statistics
San Jose State University
San Jose, CA
United States
Elham Sohrabi
Division of Mathematics and Computer Science
University of South Carolina Upstate
Spartanburg, SC
United States