Improved Maintenance of Molecular Surfaces Using Dynamic Graph Connectivity

2005 ◽  
pp. 401-413 ◽  
Author(s):  
Eran Eyal ◽  
Dan Halperin
Keyword(s):  
Graph Connectivity ◽  
Dynamic Graph ◽  
Molecular Surfaces

scholarly journals Tree Compatibility, Incomplete Directed Perfect Phylogeny, and Dynamic Graph Connectivity: An Experimental Study

Algorithms ◽  
2019 ◽  
Vol 12 (3) ◽  
pp. 53
Author(s):  
David Fernández-Baca ◽  
Lei Liu
Keyword(s):  
Data Structure ◽  
Phylogenetic Tree ◽  
Phylogenetic Trees ◽  
Computational Study ◽  
Graph Connectivity ◽  
Data Matrix ◽  
Connected Components ◽  
Perfect Phylogeny ◽  
Dynamic Graph ◽  
Tree Compatibility

We study two problems in computational phylogenetics. The first is tree compatibility. The input is a collection of phylogenetic trees over different partially-overlapping sets of species. The goal is to find a single phylogenetic tree that displays all the evolutionary relationships implied by . The second problem is incomplete directed perfect phylogeny (IDPP). The input is a data matrix describing a collection of species by a set of characters, where some of the information is missing. The question is whether there exists a way to fill in the missing information so that the resulting matrix can be explained by a phylogenetic tree satisfying certain conditions. We explain the connection between tree compatibility and IDPP and show that a recent tree compatibility algorithm is effectively a generalization of an earlier IDPP algorithm. Both algorithms rely heavily on maintaining the connected components of a graph under a sequence of edge and vertex deletions, for which they use the dynamic connectivity data structure of Holm et al., known as HDT. We present a computational study of algorithms for tree compatibility and IDPP. We show experimentally that substituting HDT by a much simpler data structure—essentially, a single-level version of HDT—improves the performance of both of these algorithm in practice. We give partial empirical and theoretical justifications for this observation.

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