Filters

635 Hits in 2.9 sec

### Polyominoes defined by two vectors

A. Del Lungo
1994 Theoretical Computer Science

### The Reconstruction of Polyominoes from Approximately Orthogonal Projections [chapter]

Maciej Gebala
2001 Lecture Notes in Computer Science
We will prove that it is NPcomplete if we reconstruct polyominoes, horizontal convex polyominoes and vertical convex polyominoes.  ...  The reconstruction of discrete two-dimensional pictures from their projection is one of the central problems in the areas of medical diagnostics, computer-aided tomography, pattern recognition, image processing  ...  In an analogous way we can define other corner regions. By P we denote the complement of P .  ...

### A note on polyomino chains with extremum general sum-connectivity index [article]

Akbar Ali, Tahir Idrees
2018 arXiv   pre-print
The general sum-connectivity index of a graph G is defined as χ_α(G)= ∑_uv∈ E(G) (d_u + d_v)^α where d_u is degree of the vertex u∈ V(G), α is a real number different from 0 and uv is the edge connecting  ...  In this note, the problem of characterizing the graphs having extremum χ_α values from a certain collection of polyomino chain graphs is solved for α<0.  ...  A polyomino chain is a polyomino system in which every square is adjacent to at most two other squares. Every polyomino chain can be represented by a graph known as polyomino chain graph.  ...

### The Number of Line-Convex Directed Polyominoes Having the Same Orthogonal Projections [chapter]

Péter Balázs
2006 Lecture Notes in Computer Science
It is proven that diagonally convex directed polyominoes are uniquely determined by their orthogonal projections. The proof of this result is algorithmical.  ...  The number of line-convex directed polyominoes with given horizontal and vertical projections is studied.  ...  Given two integers a and b such that they are coprimes and (a, b) = (0, 0) we define the kth line of the discrete rectangle R = {1, . . . , m} × {1, . . . , n} parallel to the vector (a, b) by S (a,b)  ...

### Universal Computation with Arbitrary Polyomino Tiles in Non-Cooperative Self-Assembly [chapter]

Sándor P. Fekete, Jacob Hendricks, Matthew J. Patitz, Trent A. Rogers, Robert T. Schweller
2014 Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms
We define a generalization of the abstract Tile Assembly Model (aTAM), such that a tile system consists of a collection of polyomino tiles, the Polyomino Tile Assembly Model (polyTAM), and investigate  ...  In order to prove the computational powers of polyTAM systems, we also prove a number of geometric properties held by all polyominoes of size ≥ 3.  ...  To show that Γ is simulated by some monomino system, we consider two cases. For polyomino P , let P x denote the polyomino obtained by translating P by some vector x.  ...
« Previous Showing results 1 — 15 out of 635 results