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Algorithms for Counting Minimum-Perimeter Lattice Animals

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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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Authors and Affiliations

  1. Dept. of Computer Science, The Technion—Israel Inst. of Technology, Haifa, 3200003, Israel

    Gill Barequet & Gil Ben-Shachar

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  1. Gill Barequet
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  2. Gil Ben-Shachar
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Correspondence to Gill Barequet.

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Work on this paper by both authors has been supported in part by Grant 575/15 from the Israel Science Foundation (ISF) and by Grant 2017684 from the Binational Science Foundation (BSF)

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Barequet, G., Ben-Shachar, G. Algorithms for Counting Minimum-Perimeter Lattice Animals. Algorithmica 85, 75–99 (2023). https://doi.org/10.1007/s00453-022-01008-9

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