Simplicial Complex Entropy

Dantchev, Stefan; Ivrissimtzis, Ioannis

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.

Citation

Dantchev, S., & Ivrissimtzis, I. (2016, June). Simplicial Complex Entropy. Presented at 9th International Conference on Mathematical Methods for Curves and Surfaces, Tønsberg, Norway

• Presentation Conference Type: Conference Paper (published)
• Conference Name: 9th International Conference on Mathematical Methods for Curves and Surfaces
• Start Date: Jun 23, 2016
• End Date: Jun 28, 2016
• Acceptance Date: May 16, 2017
• Online Publication Date: Oct 18, 2017
• Publication Date: Oct 18, 2017
• Deposit Date: May 12, 2017
• Publicly Available Date: Oct 18, 2018
• Print ISSN: 0302-9743
• Pages: 96-107
• Series Title: Lecture notes in computer science
• Series Number: 10521
• Series ISSN: 0302-9743,1611-3349
• Book Title: Mathematical methods for curves and surfaces : 9th International Conference, MMCS 2016, Tønsberg, Norway, June 23 - June 28, 2016. Revised selected papers.
• ISBN: 9783319678849
• DOI: https://doi.org/10.1007/978-3-319-67885-6_5
• Public URL: https://durham-repository.worktribe.com/output/1148514