scholarly journals Efficient data structure for representing and simplifying simplicial complexes in high dimensions

2011 ◽  
Author(s):  
Dominique Attali ◽  
André Lieutier ◽  
David Salinas
Keyword(s):  
Data Structure ◽  
Simplicial Complexes ◽  
High Dimensions ◽  
Efficient Data

scholarly journals EFFICIENT DATA STRUCTURE FOR REPRESENTING AND SIMPLIFYING SIMPLICIAL COMPLEXES IN HIGH DIMENSIONS

2012 ◽  
Vol 22 (04) ◽  
pp. 279-303 ◽  
Author(s):  
DOMINIQUE ATTALI ◽  
ANDRÉ LIEUTIER ◽  
DAVID SALINAS
Keyword(s):  
Data Structure ◽  
Simplicial Complex ◽  
Simplicial Complexes ◽  
Nice Property ◽  
High Dimensions ◽  
Primary Interest ◽  
Flag Complex ◽  
Edge Contraction ◽  
Efficient Data ◽  
Flag Complexes

We study the simplification of simplicial complexes by repeated edge contractions. First, we extend to arbitrary simplicial complexes the statement that edges satisfying the link condition can be contracted while preserving the homotopy type. Our primary interest is to simplify flag complexes such as Rips complexes for which it was proved recently that they can provide topologically correct reconstructions of shapes. Flag complexes (sometimes called clique complexes) enjoy the nice property of being completely determined by the graph of their edges. But, as we simplify a flag complex by repeated edge contractions, the property that it is a flag complex is likely to be lost. Our second contribution is to propose a new representation for simplicial complexes particularly well adapted for complexes close to flag complexes. The idea is to encode a simplicial complex K by the graph G of its edges together with the inclusion-minimal simplices in the set difference Flag (G)\ K. We call these minimal simplices blockers. We prove that the link condition translates nicely in terms of blockers and give formulae for updating our data structure after an edge contraction. Finally, we observe in some simple cases that few blockers appear during the simplification of Rips complexes, demonstrating the efficiency of our representation in this context.

scholarly journals The Simplex Tree: An Efficient Data Structure for General Simplicial Complexes

Algorithmica ◽  
2014 ◽  
Vol 70 (3) ◽  
pp. 406-427 ◽  
Author(s):  
Jean-Daniel Boissonnat ◽  
Clément Maria
Keyword(s):  
Data Structure ◽  
Simplicial Complexes ◽  
Efficient Data

Suffix array for multi-pattern matching with variable length wildcards

2021 ◽  
Vol 25 (2) ◽  
pp. 283-303
Author(s):  
Na Liu ◽  
Fei Xie ◽  
Xindong Wu
Keyword(s):  
Dynamic Programming ◽  
Data Structure ◽  
Pattern Matching ◽  
Edit Distance ◽  
State Of The Art ◽  
Suffix Array ◽  
Variable Length ◽  
Distance Method ◽  
Efficient Data ◽  
Comparison Algorithms

Approximate multi-pattern matching is an important issue that is widely and frequently utilized, when the pattern contains variable-length wildcards. In this paper, two suffix array-based algorithms have been proposed to solve this problem. Suffix array is an efficient data structure for exact string matching in existing studies, as well as for approximate pattern matching and multi-pattern matching. An algorithm called MMSA-S is for the short exact characters in a pattern by dynamic programming, while another algorithm called MMSA-L deals with the long exact characters by the edit distance method. Experimental results of Pizza & Chili corpus demonstrate that these two newly proposed algorithms, in most cases, are more time-efficient than the state-of-the-art comparison algorithms.

Storage-efficient data structure for large lookup dictionaries

1996 ◽  
Vol 58 (4) ◽  
pp. 201-206 ◽  
Author(s):  
Vishv M. Malhotra ◽  
Bala Srinivasan ◽  
Santosh Kulkarni
Keyword(s):  
Data Structure ◽  
Efficient Data
Sign in / Sign up

Export Citation Format

Share Document