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Polynomial Graph Parsing with Non-Structural Reentrancies ...
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The Linear Arrangement Library. A new tool for research on syntactic dependency structures ...
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Complete Variable-Length Codes: An Excursion into Word Edit Operations
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In: LATA 2020 ; https://hal.archives-ouvertes.fr/hal-02389403 ; LATA 2020, Mar 2020, Milan, Italy (2020)
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The relationship between word complexity and computational complexity in subshifts
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In: https://hal.archives-ouvertes.fr/hal-02063174 ; 2019 (2019)
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Edge crossings in random linear arrangements ...
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Abstract:
In spatial networks vertices are arranged in some space and edges may cross. When arranging vertices in a 1-dimensional lattice edges may cross when drawn above the vertex sequence as it happens in linguistic and biological networks. Here we investigate the general of problem of the distribution of edge crossings in random arrangements of the vertices. We generalize the existing formula for the expectation of this number in random linear arrangements of trees to any network and derive an expression for the variance of the number of crossings in an arbitrary layout relying on a novel characterization of the algebraic structure of that variance in an arbitrary space. We provide compact formulae for the expectation and the variance in complete graphs, complete bipartite graphs, cycle graphs, one-regular graphs and various kinds of trees (star trees, quasi-star trees and linear trees). In these networks, the scaling of expectation and variance as a function of network size is asymptotically power-law-like in ... : Generalised our theory from one-dimensional layouts to practically any type of layout. This helps study the variance of the number of crossings in graphs when their vertices are arranged on the surface of a sphere, or on the plane. Moreover, we also give closed formulae for this variance on particular types of graphs in both linear arrangements and general layouts ...
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Keyword:
Combinatorics math.CO; Discrete Mathematics cs.DM; FOS Computer and information sciences; FOS Mathematics; FOS Physical sciences; Physics and Society physics.soc-ph
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URL: https://dx.doi.org/10.48550/arxiv.1910.03926 https://arxiv.org/abs/1910.03926
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Avoiding or limiting regularities in words
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In: Sequences, Groups and Number Theory ; https://hal-lirmm.ccsd.cnrs.fr/lirmm-02083655 ; Sequences, Groups and Number Theory, pp.177-212, 2018, 978-3-319-69151-0. ⟨10.1007/978-3-319-69152-7_5⟩ (2018)
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Tools for the analysis of noisy discrete curves ; Outils pour l'analyse des courbes discrètes bruitées
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In: https://tel.archives-ouvertes.fr/tel-01947024 ; Géométrie algorithmique [cs.CG]. Université de Lorraine, 2018. Français. ⟨NNT : 2018LORR0159⟩ (2018)
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K4-free Graphs as a Free Algebra
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In: 42nd International Symposium on Mathematical Foundations of Computer Science ; https://hal.archives-ouvertes.fr/hal-01515752 ; 42nd International Symposium on Mathematical Foundations of Computer Science, Aug 2017, Aalborg, Denmark (2017)
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Matroids Hitting Sets and Unsupervised Dependency Grammar Induction ...
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Parsing with Traces: An $O(n^4)$ Algorithm and a Structural Representation ...
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Palindromic language of thin discrete planes
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In: ISSN: 1879-2294 ; EISSN: 0304-3975 ; Theoretical Computer Science ; https://hal.archives-ouvertes.fr/hal-01262289 ; Theoretical Computer Science, Elsevier, 2016, pp.101-108. ⟨10.1016/j.tcs.2015.11.023⟩ (2016)
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Synchronizing Relations on Words
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In: ISSN: 1432-4350 ; EISSN: 1433-0490 ; Theory of Computing Systems ; https://hal.archives-ouvertes.fr/hal-01778459 ; Theory of Computing Systems, Springer Verlag, 2015, 57 (2), pp.287 - 318. ⟨10.1007/s00224-014-9584-2⟩ (2015)
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