Algorithms for Counting Minimum-Perimeter Lattice Animals

Gill Barequet; Gil Ben-Shachar

doi:10.1007/s00453-022-01008-9

Algorithms for Counting Minimum-Perimeter Lattice Animals

Gill Barequet, Gil Ben-Shachar

Computer Science

Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

A 2-dimensional lattice animal is a set of edge-connected cells on some lattice. In this paper, we address the problem of counting minimum-perimeter lattice animals, that is, animals that have the minimum possible perimeter of all animals of the same area. We provide two types of algorithms for counting minimum-perimeter animals on two lattices, namely, the square and hexagonal lattices, and analyze and compare the algorithms.

Original language	English
Pages (from-to)	75-99
Number of pages	25
Journal	Algorithmica
Volume	85
Issue number	1
DOIs	https://doi.org/10.1007/s00453-022-01008-9
State	Published - Jan 2023

Keywords

Lattice animals
Polyhexes
Polyiamonds
Polyominoes

All Science Journal Classification (ASJC) codes

General Computer Science
Applied Mathematics
Computer Science Applications

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10.1007/s00453-022-01008-9

Cite this

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abstract = "A 2-dimensional lattice animal is a set of edge-connected cells on some lattice. In this paper, we address the problem of counting minimum-perimeter lattice animals, that is, animals that have the minimum possible perimeter of all animals of the same area. We provide two types of algorithms for counting minimum-perimeter animals on two lattices, namely, the square and hexagonal lattices, and analyze and compare the algorithms.",

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AB - A 2-dimensional lattice animal is a set of edge-connected cells on some lattice. In this paper, we address the problem of counting minimum-perimeter lattice animals, that is, animals that have the minimum possible perimeter of all animals of the same area. We provide two types of algorithms for counting minimum-perimeter animals on two lattices, namely, the square and hexagonal lattices, and analyze and compare the algorithms.

KW - Lattice animals

KW - Polyhexes

KW - Polyiamonds

KW - Polyominoes

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Algorithms for Counting Minimum-Perimeter Lattice Animals

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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