Optimal Partial Tiling of Manhattan Polyominoes

Finding an efficient optimal partial tiling algorithm is still an open problem. We have worked on a special case, the tiling of Manhattan polyominoes with dominoes, for which we give an algorithm linear in the number of columns. Some techniques are borrowed from traditional graph optimisation problems. For our purpose, a polyomino is the (non necessarily connected) union of unit squares (for which we will consider the vertices to be in Z2 ) and a domino is a polyomino with two edge-adjacent unit squares. To solve the domino tiling problem [6,9,10,11,12,13] for a polyomino P is equivalent to finding a perfect matching in the edge-adjacent graph Gp of P’s unit squares. A specific point of view to study tiling problems has been introduced by Conway and Lagarias in [4]: they transformed the tiling problem into a combinatorial group theory problem. Thurston [13] built on this idea by introducing the notion of height, with which he devised a linear-time algorithm to tile a polyomino with...

• Type: Conference
• Year: 2009
• Where: DGCI
• Authors: Olivier Bodini, Jérémie Lumbroso
• Keywords: Algorithm, DGCI 2009, Discrete Geometry, Optimal Partial Tiling, Tiling Problem