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Simplicial complex entropy.

Dantchev, Stefan and Ivrissimtzis, Ioannis (2017) 'Simplicial complex entropy.', in Mathematical methods for curves and surfaces : 9th International Conference, MMCS 2016, Tønsberg, Norway, June 23 - June 28, 2016. Revised selected papers. Cham: Springer, pp. 96-107. Lecture notes in computer science. (10521).

Abstract

We propose an entropy function for simplicial complices. Its value gives the expected cost of the optimal encoding of sequences of vertices of the complex, when any two vertices belonging to the same simplex are indistinguishable. We focus on the computational properties of the entropy function, showing that it can be computed efficiently. Several examples over complices consisting of hundreds of simplices show that the proposed entropy function can be used in the analysis of large sequences of simplicial complices that often appear in computational topology applications.

Item Type:Book chapter
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1007/978-3-319-67885-6_5
Publisher statement:The final publication is available at Springer via https://doi.org/10.1007/978-3-319-67885-6_5
Date accepted:16 May 2017
Date deposited:15 May 2017
Date of first online publication:18 October 2017
Date first made open access:18 October 2018

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