Improved Practical Algorithms for Rooted Subtree Prune and Regraft (rSPR) Distance and Hybridization Number

2020 ◽  
Vol 27 (9) ◽  
pp. 1422-1432
Author(s):  
Kohei Yamada ◽  
Zhi-zhong Chen ◽  
Lusheng Wang
2019 ◽  
Vol 50 (11-12) ◽  
pp. 1204-1213 ◽  
Author(s):  
Gaëlle Varkas ◽  
Clio Ribbens ◽  
Edouard Louis ◽  
Filip Van den Bosch ◽  
Rik Lories ◽  
...  

2021 ◽  
Vol 82 (1-2) ◽  
Author(s):  
Lena Collienne ◽  
Alex Gavryushkin

AbstractMany popular algorithms for searching the space of leaf-labelled (phylogenetic) trees are based on tree rearrangement operations. Under any such operation, the problem is reduced to searching a graph where vertices are trees and (undirected) edges are given by pairs of trees connected by one rearrangement operation (sometimes called a move). Most popular are the classical nearest neighbour interchange, subtree prune and regraft, and tree bisection and reconnection moves. The problem of computing distances, however, is $${\mathbf {N}}{\mathbf {P}}$$ N P -hard in each of these graphs, making tree inference and comparison algorithms challenging to design in practice. Although anked phylogenetic trees are one of the central objects of interest in applications such as cancer research, immunology, and epidemiology, the computational complexity of the shortest path problem for these trees remained unsolved for decades. In this paper, we settle this problem for the ranked nearest neighbour interchange operation by establishing that the complexity depends on the weight difference between the two types of tree rearrangements (rank moves and edge moves), and varies from quadratic, which is the lowest possible complexity for this problem, to $${\mathbf {N}}{\mathbf {P}}$$ N P -hard, which is the highest. In particular, our result provides the first example of a phylogenetic tree rearrangement operation for which shortest paths, and hence the distance, can be computed efficiently. Specifically, our algorithm scales to trees with tens of thousands of leaves (and likely hundreds of thousands if implemented efficiently).


2012 ◽  
Vol 29 (4) ◽  
pp. 428-434 ◽  
Author(s):  
N. Donmez ◽  
M. Brudno
Keyword(s):  

2009 ◽  
Vol 76 (9) ◽  
pp. 921-922
Author(s):  
Martin A. Nash

2018 ◽  
Vol 7 (4) ◽  
pp. R135-R146 ◽  
Author(s):  
Efstratios Kardalas ◽  
Stavroula A Paschou ◽  
Panagiotis Anagnostis ◽  
Giovanna Muscogiuri ◽  
Gerasimos Siasos ◽  
...  

Hypokalemia is a common electrolyte disturbance, especially in hospitalized patients. It can have various causes, including endocrine ones. Sometimes, hypokalemia requires urgent medical attention. The aim of this review is to present updated information regarding: (1) the definition and prevalence of hypokalemia, (2) the physiology of potassium homeostasis, (3) the various causes leading to hypokalemia, (4) the diagnostic steps for the assessment of hypokalemia and (5) the appropriate treatment of hypokalemia depending on the cause. Practical algorithms for the optimal diagnostic, treatment and follow-up strategy are presented, while an individualized approach is emphasized.


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