7 papers · 1 filter
Lozenge Tiling by Computing Distances
Jean-Marie Favreau, Yan Gerard, Pascal Lafourcade +1
The Calisson puzzle is a tiling puzzle in which one must tile a triangular grid inside a hexagon with lozenges, under the constraint that certain prescribed edges remain tile bound…
Short Flip Sequences to Untangle Segments in the Plane
Guilherme D. da Fonseca, Yan Gerard, Bastien Rivier
A (multi)set of segments in the plane may form a TSP tour, a matching, a tree, or any multigraph. If two segments cross, then we can reduce the total length with the following flip…
The Calissons Puzzle
Jean-Marie Favreau, Yan Gerard, Pascal Lafourcade +1
In 2022, Olivier Longuet, a French mathematics teacher, created a game called the \textit{calissons puzzle}. Given a triangular grid in a hexagon and some given edges of the grid,…
Conflict Optimization for Binary CSP Applied to Minimum Partition into Plane Subgraphs and Graph Coloring
Loïc Crombez, Guilherme D. da Fonseca, Florian Fontan +8
CG:SHOP is an annual geometric optimization challenge and the 2022 edition proposed the problem of coloring a certain geometric graph defined by line segments. Surprisingly, the to…
Efficient Algorithms for Battleship
Loïc Crombez, Guilherme D. da Fonseca, Yan Gerard
We consider an algorithmic problem inspired by the Battleship game. In the variant of the problem that we investigate, there is a unique ship of shape which has bee…
Efficient Algorithms to Test Digital Convexity
Loïc Crombez, Guilherme D. da Fonseca, Yan Gérard
A set is digital convex if , where denotes the convex hull of . In this paper, we consider the algorithmic prob…