A heuristic approach to domino grid problem

• Published in: Indian journal of pure and applied mathematics Vol. 54; no. 4; pp. 1056 - 1068
• Main Authors: Nabiyev, Vasif V., Pehlivan, Hüseyin
• Format: Journal Article
• Language: English
• Published: New Delhi Indian National Science Academy 01.12.2023; Springer Nature B.V
• Subjects: Applications of Mathematics; Combinatorial analysis; Graph theory; Graphical representations; Heuristic methods; Mathematics; Mathematics and Statistics; Numerical Analysis; Original Research; Search methods; Tiling; Domino tiling; Enumeration; 05B45; 05B50; 90C59; Heuristic search; 90C27; Perfect matching; 05A15; Bigraphs
• ISSN: 0019-5588; 0975-7465
• DOI: 10.1007/s13226-022-00321-x

Dominoes have been the main subject of many theoretical and practical studies, which have primarily focused on the solutions to domino tiling problems. The domino grid problem is a different type of tiling problems in which the aim is to find a complete set of dominoes on a two-dimensional grid arranged in a patternless fashion. Tiling problems are generally solved using combinatorial search methods because the grid can be organized into a large number of possible domino patterns. This paper addresses an efficient solution to the domino grid problem, using a heuristic approach governed by some state-specific rules. The problem is represented by a bipartite graph and a possible solution is obtained by computing a perfect matching in the graph, based on the degrees and positions of dominoes. For different grid layouts, the search space of the problem is explored, enumerating the total number of state evaluations required to generate all possible solutions.