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Generalized Fibonacci Cubes Based on Swap and Mismatch Distance

Authors Marcella Anselmo , Giuseppa Castiglione , Manuela Flores , Dora Giammarresi , Maria Madonia , Sabrina Mantaci

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OASIcs.Grossi.5.pdf
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ACM Subject Classification
  • Mathematics of computing → Combinatorics on words
  • Theory of computation → Design and analysis of algorithms
  • Theory of computation → Formal languages and automata theory
Keywords
  • Swap and mismatch distance
  • Isometric words
  • Hypercube

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Abstract

The hypercube of dimension n is the graph with 2ⁿ vertices associated to all binary words of length n and edges connecting pairs of vertices with Hamming distance equal to 1. Here, an edit distance based on swaps and mismatches is considered and referred to as tilde-distance. Accordingly, the tilde-hypercube is defined, with edges linking words having tilde-distance equal to 1. The focus is on the subgraphs of the tilde-hypercube obtained by removing all vertices having a given word as factor. If the word is 11, then the subgraph is called tilde-Fibonacci cube; in the case of a generic word, it is called generalized tilde-Fibonacci cube. The paper surveys recent results on the definition and characterization of those words that define generalized tilde-Fibonacci cubes that are isometric subgraphs of the tilde-hypercube. Finally, a special attention is given to the study of the tilde-Fibonacci cubes.

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Marcella Anselmo, Giuseppa Castiglione, Manuela Flores, Dora Giammarresi, Maria Madonia, and Sabrina Mantaci. Generalized Fibonacci Cubes Based on Swap and Mismatch Distance. In From Strings to Graphs, and Back Again: A Festschrift for Roberto Grossi's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 132, pp. 5:1-5:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/OASIcs.Grossi.5

Author Details

Marcella Anselmo
  • Dipartimento di Informatica, Università di Salerno, Italy
Giuseppa Castiglione
  • Dipartimento di Matematica e Informatica, Università di Palermo, Italy
Manuela Flores
  • Dipartimento di Bioscienze e Territorio, Università del Molise, Campobasso, Italy
Dora Giammarresi
  • Dipartimento di Matematica, Università Roma "Tor Vergata", Italy
Maria Madonia
  • Dipartimento di Matematica e Informatica, Università di Catania, Italy
Sabrina Mantaci
  • Dipartimento di Matematica e Informatica, Università di Palermo, Italy

Funding

Partially supported by INdAM-GNCS Project 2025 - CUP E53C24001950001, FARB Project ORSA240597 of University of Salerno, TEAMS Project and PNRR MUR Project PE0000013-FAIR University of Catania, FFR fund University of Palermo, MUR Excellence Department Project MatMod@TOV, CUP E83C23000330006, awarded to the Department of Mathematics, University of Rome Tor Vergata, “ACoMPA – Algorithmic and Combinatorial Methods for Pangenome Analysis” (CUP B73C24001050001) funded by the NextGeneration EU programme PNRR ECS00000017 Tuscany Health Ecosystem (Spoke 6).

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