Leaf realization problem, caterpillar graphs and prefix normal words

Massé, Alexandre Blondin; Carufel, Julien de; Goupil, Alain; Lapointe, Mélodie; Nadeau, Émile; Vandomme, Elise

doi:10.1016/j.tcs.2018.04.019

Cited by 10 publications

(9 citation statements)

References 28 publications

(46 reference statements)

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“…Cicalese et al gave a generation algorithm in [15], with linear running time per word, and studied infinite prefix normal words in [16]. Prefix normal words and prefix normal forms have been applied to a certain family of graphs by Blondin-Massé et al [7], and were shown to pertain to a new class of languages connected to the Reflected Binary Gray Code by Sawada et al [29]. Very recently, Fleischmann et al presented some results on the size of the equivalence classes in [?…”

Section: Related Workmentioning

confidence: 99%

Generating a Gray code for prefix normal words in amortized polylogarithmic time per word

Burcsi

Fici²,

Lipták

et al. 2020

Preprint

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A prefix normal word is a binary word with the property that no substring has more 1s than the prefix of the same length. By proving that the set of prefix normal words is a bubble language, we can exhaustively list all prefix normal words of length n as a combinatorial Gray code, where successive strings differ by at most two swaps or bit flips. This Gray code can be generated in O(log 2 n) amortized time per word, while the best generation algorithm hitherto has O(n) running time per word. We also present a membership tester for prefix normal words, as well as a novel characterization of bubble languages.

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Section: Related Workmentioning

confidence: 99%

Generating a Gray code for prefix normal words in amortized polylogarithmic time per word

Burcsi

Fici²,

Lipták

et al. 2020

Preprint

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show abstract

“…In particular, since they have a linear structure, they might be interpreted as words embedded in graphs. For instance, in [3], the second author of this article and his co-authors established a link between the leaf function of caterpillar graphs and prexnormal words, a family of words closely related to the bubble sort [7].…”

Section: Introductionmentioning

confidence: 99%

The Leaf Function of Graphs Associated with Penrose Tilings

Porrier

2020

IJGC

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In graph theory, the question of fully leafed induced subtrees has recently been investigated by Blondin Massé et al in regular tilings of the Euclidian plane and 3-dimensional space. The function LG that gives the maximum number of leaves of an induced subtree of a graph $G$ of order $n$, for any $n\in \N$, is called leaf function. This article is a first attempt at studying this problem in non-regular tilings, more specifically Penrose tilings. We rely not only on geometric properties of Penrose tilings, that allow us to find an upper bound for the leaf function in these tilings, but also on their links to the Fibonacci word, which give us a lower bound. Our approach rely on a purely discrete representation of points in the tilings, thus preventing numerical errors and improving computation efficiency. Finally, we present a procedure to dynamically generate induced subtrees without having to generate the whole patch surrounding them.

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“…Prefix normal words were introduced by G. Fici and Z. Lipták in [4] because of their connection to binary jumbled pattern matching. Recently, prefix normal words have been used because of their connection to trees with a prescribed number of vertices and leaves in caterpillar graphs [6].…”

Section: Introductionmentioning

confidence: 99%