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

Access to Document

10.1007/s00453-022-01008-9

Cite this

@article{2e2572db20bb4b17985e78f58fb3f903,

title = "Algorithms for Counting Minimum-Perimeter Lattice Animals",

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.",

keywords = "Lattice animals, Polyhexes, Polyiamonds, Polyominoes",

author = "Gill Barequet and Gil Ben-Shachar",

note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.",

year = "2023",

month = jan,

doi = "10.1007/s00453-022-01008-9",

language = "الإنجليزيّة",

volume = "85",

pages = "75--99",

journal = "Algorithmica",

issn = "0178-4617",

publisher = "Springer New York",

number = "1",

}

TY - JOUR

T1 - Algorithms for Counting Minimum-Perimeter Lattice Animals

AU - Barequet, Gill

AU - Ben-Shachar, Gil

PY - 2023/1

Y1 - 2023/1

N2 - 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.

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

UR - http://www.scopus.com/inward/record.url?scp=85135570397&partnerID=8YFLogxK

U2 - 10.1007/s00453-022-01008-9

DO - 10.1007/s00453-022-01008-9

M3 - مقالة

SN - 0178-4617

VL - 85

SP - 75

EP - 99

JO - Algorithmica

JF - Algorithmica

IS - 1

ER -

Algorithms for Counting Minimum-Perimeter Lattice Animals

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Cite this