scholarly journals Maximum parsimony distance on phylogenetic trees: A linear kernel and constant factor approximation algorithm

2021 ◽  
Vol 117 ◽  
pp. 165-181
Author(s):  
Mark Jones ◽  
Steven Kelk ◽  
Leen Stougie
Keyword(s):  
Approximation Algorithm ◽  
Maximum Parsimony ◽  
Phylogenetic Trees ◽  
Constant Factor ◽  
Linear Kernel

scholarly journals Constant factor approximation algorithm for TSP satisfying a biased triangle inequality

2017 ◽  
Vol 657 ◽  
pp. 111-126 ◽  
Author(s):  
Usha Mohan ◽  
Sivaramakrishnan Ramani ◽  
Sounaka Mishra
Keyword(s):  
Approximation Algorithm ◽  
Triangle Inequality ◽  
Constant Factor

scholarly journals Randomized heuristic for the maximum clique problem

2020 ◽  
Author(s):  
Shalin Shah
Keyword(s):  
Approximation Algorithm ◽  
Randomized Algorithm ◽  
Maximum Clique ◽  
Constant Factor ◽  
Maximum Clique Problem ◽  
Hard Problem ◽  
Np Hard ◽  
Np Hard Problem ◽  
Java Code ◽  
Clique Problem

<p>A clique in a graph is a set of vertices that are all directly connected</p><p>to each other i.e. a complete sub-graph. A clique of the largest size is</p><p>called a maximum clique. Finding the maximum clique in a graph is an</p><p>NP-hard problem and it cannot be solved by an approximation algorithm</p><p>that returns a solution within a constant factor of the optimum. In this</p><p>work, we present a simple and very fast randomized algorithm for the</p><p>maximum clique problem. We also provide Java code of the algorithm</p><p>in our git repository. Results show that the algorithm is able to find</p><p>reasonably good solutions to some randomly chosen DIMACS benchmark</p><p>graphs. Rather than aiming for optimality, we aim to find good solutions</p><p>very fast.</p>

scholarly journals Randomized heuristic for the maximum clique problem

2020 ◽  
Author(s):  
Shalin Shah
Keyword(s):  
Approximation Algorithm ◽  
Randomized Algorithm ◽  
Maximum Clique ◽  
Constant Factor ◽  
Maximum Clique Problem ◽  
Hard Problem ◽  
Np Hard ◽  
Np Hard Problem ◽  
Java Code ◽  
Clique Problem

<p>A clique in a graph is a set of vertices that are all directly connected</p><p>to each other i.e. a complete sub-graph. A clique of the largest size is</p><p>called a maximum clique. Finding the maximum clique in a graph is an</p><p>NP-hard problem and it cannot be solved by an approximation algorithm</p><p>that returns a solution within a constant factor of the optimum. In this</p><p>work, we present a simple and very fast randomized algorithm for the</p><p>maximum clique problem. We also provide Java code of the algorithm</p><p>in our git repository. Results show that the algorithm is able to find</p><p>reasonably good solutions to some randomly chosen DIMACS benchmark</p><p>graphs. Rather than aiming for optimality, we aim to find good solutions</p><p>very fast.</p>

scholarly journals A generalized Robinson-Foulds distance for labeled trees

BMC Genomics ◽  
2020 ◽  
Vol 21 (S10) ◽  
Author(s):  
Samuel Briand ◽  
Christophe Dessimoz ◽  
Nadia El-Mabrouk ◽  
Manuel Lafond ◽  
Gabriela Lobinska
Keyword(s):  
Approximation Algorithm ◽  
Phylogenetic Trees ◽  
Linear Time ◽  
Crucial Aspect ◽  
Labeled Trees ◽  
Link Type

Abstract Background The Robinson-Foulds (RF) distance is a well-established measure between phylogenetic trees. Despite a lack of biological justification, it has the advantages of being a proper metric and being computable in linear time. For phylogenetic applications involving genes, however, a crucial aspect of the trees ignored by the RF metric is the type of the branching event (e.g. speciation, duplication, transfer, etc). Results We extend RF to trees with labeled internal nodes by including a node flip operation, alongside edge contractions and extensions. We explore properties of this extended RF distance in the case of a binary labeling. In particular, we show that contrary to the unlabeled case, an optimal edit path may require contracting “good” edges, i.e. edges shared between the two trees. Conclusions We provide a 2-approximation algorithm which is shown to perform well empirically. Looking ahead, computing distances between labeled trees opens up a variety of new algorithmic directions.Implementation and simulations available at https://github.com/DessimozLab/pylabeledrf.

A constant-factor approximation algorithm for multi-vehicle collection for processing problem

2012 ◽  
Vol 7 (7) ◽  
pp. 1627-1642
Author(s):  
E. Yücel ◽  
F. S. Salman ◽  
E. L. Örmeci ◽  
E. S. Gel
Keyword(s):  
Approximation Algorithm ◽  
Constant Factor ◽  
Processing Problem
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