Tour covering for solid staircase grids and rectangular grids with holes

Determine optimal coverings by length-constrained tours for solid staircase grid graphs and rectangular grid graphs with holes, including the minimum number of tours and the minimum total tour length.

Background

The paper develops linear-time algorithms for the two tour-covering objectives on rectangular grid graphs without holes when the base station is at a corner. In the conclusion, the authors identify two graph families outside that solved setting—solid staircase grid graphs and rectangular grid graphs containing holes—for which the same covering problems remain unresolved.