Pareto-Optimal Domino-Tiling of Orthogonal Polygon Phased Arrays

Conformal invariance of domino tiling

The complexity of domino tiling

In this paper, we study the problem of how to tile a layout with dominoes. For non-coloured dominoes, this can be determined easily by testing whether the layout graph has a perfect matching. We study here tiling with coloured dominoes, where colours of adjacent dominoes must match. It was known that this problem is NP-hard when the layout graph is a tree. We first strengthen this NP-hardness r...

Domino Tiling Congruence Modulo 4

The number of domino tilings of a region with reflective symmetry across a line is combinatorially shown to depend on the number of domino tilings of particular subregions, modulo 4. This expands upon previous congruency results for domino tilings, modulo 2, and leads to a variety of corollaries, including that the number of domino tilings of a k× 2k rectangle is congruent to 1 mod 4.

Tiling a Polygon with Rectangles

We study the problem of tiling a simple polygon of surface n with rectangles of given types (tiles). We present a linear time algorithm for deciding if a polygon can be tiled with 1 m and k 1 tiles (and giving a tiling when it exists), and a quadratic algorithm for the same problem when the tile types are m k and k m.

The Complexity of Domino Tiling Problems

In this paper, we give a combinatorial formalization that describes a wide range of related problems in the theory of tiling derived from the popular game of dominos. We show that determining if a given finite region of the plane can be tiled with a given set of dominos is NP-Complete. The new graph theoretical methods we introduce allow this result to be easily generalized to a variety of simi...