Minimal-perimeter polyominoes: chains, roots, and algorithms

Gill Barequet, Gil Ben-Shachar

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


A polyomino is a set of edge-connected squares on the square lattice. We investigate the combinatorial and geometric properties of minimal-perimeter polyominoes. We explore the behavior of minimal-perimeter polyominoes when they are “inflated,” i.e., expanded by all empty cells neighboring them, and show that inflating all minimal-perimeter polyominoes of a given area create the set of all minimal-perimeter polyominoes of some larger area. We characterize the roots of the infinite chains of sets of minimal-perimeter polyominoes which are created by inflating polyominoes of another set of minimal-perimeter polyominoes, and show that inflating any polyomino for a sufficient amount of times results in a minimal-perimeter polyomino. In addition, we devise two efficient algorithms for counting the number of minimal-perimeter polyominoes of a given area, compare the algorithms and analyze their running times, and provide the counts of polyominoes which they produce.

Original languageEnglish
Title of host publicationAlgorithms and Discrete Applied Mathematics - 5th International Conference, CALDAM 2019, Proceedings
EditorsSudebkumar Prasant Pal, Ambat Vijayakumar
Number of pages15
StatePublished - 2019
Event5th International Conference on Algorithms and Discrete Applied Mathematics, CALDAM 2019 - Kharagpur, India
Duration: 14 Feb 201916 Feb 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11394 LNCS


Conference5th International Conference on Algorithms and Discrete Applied Mathematics, CALDAM 2019

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)


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