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Testing Convexity Properties of Tree Colorings

Eldar Fischer, Orly Yahalom
2009 Algorithmica  
We give a 1-sided, non-adaptive, distribution-free -test for the convexity of tree colorings.  ...  Our results concern the important subcase of testing for convexity in trees.  ...  Acknowledgements We thank Sagi Snir for introducing us to the topic of phylogenetic trees. We also thank Ronitt Rubinfeld for helpful comments.  ... 
doi:10.1007/s00453-009-9368-2 fatcat:pmm3xzizb5bejgc53g45gre4xu

Testing Convexity Properties of Tree Colorings [chapter]

Eldar Fischer, Orly Yahalom
STACS 2007  
We give a 1-sided, non-adaptive, distribution-free -test for the convexity of tree colorings.  ...  Our results concern the important subcase of testing for convexity in trees.  ...  Acknowledgements We thank Sagi Snir for introducing us to the topic of phylogenetic trees. We also thank Ronitt Rubinfeld for helpful comments.  ... 
doi:10.1007/978-3-540-70918-3_10 dblp:conf/stacs/FischerY07 fatcat:ljfvxcapand3tamitx6tjfs2iy

Page 10260 of Mathematical Reviews Vol. , Issue 2004m [page]

2004 Mathematical Reviews  
In addition we have an algorithm that tests whether a function f:[n]— R is convex (concave) with running time of O((logn)/e).”  ...  The authors also extend the testing algorithms to solve the relaxed versions of the related search problems of all properties presented above.  ... 

Point-Set Embeddability of 2-Colored Trees [chapter]

Fabrizio Frati, Marc Glisse, William J. Lenhart, Giuseppe Liotta, Tamara Mchedlidze, Rahnuma Islam Nishat
2013 Lecture Notes in Computer Science  
of 2-colored trees (resp. 2-colored binary trees).  ...  Finally, we show that universal convex point sets with n points exist for 1-bend bichromatic point-set embeddings of 2-colored trees. W. Didimo and M.  ...  We have shown that testing the bichromatic point-set embeddability of a 2-colored tree on a convex point set is an N P-complete problem.  ... 
doi:10.1007/978-3-642-36763-2_26 fatcat:vapgn5bqv5f2pp3rovqpsdasaa

A linear-time algorithm for computing the voronoi diagram of a convex polygon

Alok Aggarwal, Leonidas J. Guibas, James Saxe, Peter W. Shor
1989 Discrete & Computational Geometry  
We present an algorithm for computing certain kinds of threedimensional convex hulls in linear time.  ...  Using this algorithm, we show that the Voronoi diagram of n sites in the plane can be computed in O(n) time when these sites form the vertices of a convex polygon in, say, counterclockwise order.  ...  Fig. 3 .Fig. 4 . 34 The transitivity property of the tetrahedron test, The topological ordering of vertices around a tree. Fig. 5 . 5 Case (a)--leaf nodes. Fig. 6 . 6 Case (b)--comb nodes.  ... 
doi:10.1007/bf02187749 fatcat:imdybpi2lfh65izvvqu5woeneu

Page 924 of Mathematical Reviews Vol. , Issue 83c [page]

1983 Mathematical Reviews  
The graph H is defined by a Tremaux tree of G (maximal depth-first-search subtree of G). The method is to test whether these edges form a cocycle of H.  ...  Properties involving embeddings and colorings of graphs have been extensively studied.  ... 

The complexity of minimum convex coloring

Frank Kammer, Torsten Tholey
2012 Discrete Applied Mathematics  
A coloring of the vertices of a graph is called convex if each subgraph induced by all vertices of the same color is connected.  ...  Two variants of the problem are shown to be N P-hard on trees even if in the initial coloring each color is used to color only a bounded number of vertices.  ...  However, each convex recoloring C opt of optimal cost either is a recoloring with property (D,c) or it colors w.l.o.g. exactly one vertex u with c.  ... 
doi:10.1016/j.dam.2011.09.022 fatcat:g2wesaystjdbppt4dxvsd4u4ca

The Complexity of Minimum Convex Coloring [chapter]

Frank Kammer, Torsten Tholey
2008 Lecture Notes in Computer Science  
A coloring of the vertices of a graph is called convex if each subgraph induced by all vertices of the same color is connected.  ...  Two variants of the problem are shown to be N P-hard on trees even if in the initial coloring each color is used to color only a bounded number of vertices.  ...  However, each convex recoloring C opt of optimal cost either is a recoloring with property (D,c) or it colors w.l.o.g. exactly one vertex u with c.  ... 
doi:10.1007/978-3-540-92182-0_5 fatcat:ttifb5jzsvdmph2q3fdlf7l6cu

Convex contouring of volumetric data

Tao Ju, Scott Schaefer, Joe Warren
2003 The Visual Computer  
Using the same technique, we can perform fast, crack-free multi-resolution contouring on nested grids of volumetric data.  ...  The decision trees determine triangulations dynamically by values at cell corners.  ...  These tests can be organized in a decision tree structure, introduced in the last section. Different sets of tests result in differently shaped decision trees.  ... 
doi:10.1007/s00371-003-0216-0 fatcat:ocwagabblnfmlm5m3jghnn67ua

An extended formulation of the convex recoloring problem on a tree

Sunil Chopra, Bartosz Filipecki, Kangbok Lee, Minseok Ryu, Sangho Shim, Mathieu Van Vyve
2016 Mathematical programming  
We introduce a strong extended formulation of the convex recoloring problem on a tree, which has an application in analyzing phylogenetic trees.  ...  We also show that the natural restriction of the extended formulation provides a complete inequality description of the polytope of subtrees of a tree.  ...  Acknowledgements We thank Professor Yoshiko Wakabayashi and the other authors of [4] for sharing their data. We are of course grateful for their paper that inspired our work.  ... 
doi:10.1007/s10107-016-1094-3 fatcat:3yotlteogjbixehzcfchuuo2ty

Reconciling taxonomy and phylogenetic inference: formalism and algorithms for describing discord and inferring taxonomic roots [article]

Frederick A. Matsen, Aaron Gallagher
2011 arXiv   pre-print
Although taxonomy is often used informally to evaluate the results of phylogenetic inference and find the root of phylogenetic trees, algorithmic methods to do so are lacking.  ...  We also develop a formalism and an algorithm for rooting phylogenetic trees according to a taxonomy. All of these algorithms are implemented in freely-available software.  ...  the COG trees to be used as test data for our algorithm.  ... 
arXiv:1109.5423v2 fatcat:wnuwxlelafaavd4z5zbuwx6gnu

Reconciling taxonomy and phylogenetic inference: formalism and algorithms for describing discord and inferring taxonomic roots

Frederick A Matsen, Aaron Gallagher
2012 Algorithms for Molecular Biology  
Although taxonomy is often used informally to evaluate the results of phylogenetic inference and the root of phylogenetic trees, algorithmic methods to do so are lacking.  ...  This algorithm improves upon the current best algorithm in terms of asymptotic complexity for the parameter regime of interest; we also describe a branch-and-bound algorithm that saves orders of magnitude  ...  the COG trees to be used as test data for our algorithm.  ... 
doi:10.1186/1748-7188-7-8 pmid:22549005 pmcid:PMC3384453 fatcat:ebrn4y2yv5dolal6vmfkv4yle4

Ramified Rectilinear Polygons: Coordinatization by Dendrons

Hans-Jürgen Bandelt, Victor Chepoi, David Eppstein
2015 Discrete & Computational Geometry  
The rectangular cell complexes that share this same embedding property are called ramified rectilinear polygons.  ...  The links of vertices in these cell complexes may be arbitrary bipartite graphs, in contrast to simple rectilinear polygons where the links of points are either 4-cycles or paths of length at most 3.  ...  Employing the induction hypothesis to the coloring of the subgraph of G induced by the convex set B 1 , we conclude that H i is indeed a tree.  ... 
doi:10.1007/s00454-015-9743-5 fatcat:yk7svrt4azarlmu5faonckwu2e

MapSets: Visualizing Embedded and Clustered Graphs

Alon Efrat, Yifan Hu, Stephen Kobourov, Sergey Pupyrev
2015 Journal of Graph Algorithms and Applications  
The proposed method relies on a theoretically sound geometric algorithm which guarantees the contiguity and disjointness of the regions representing the clusters, and also optimizes the convexity of the  ...  We thank the authors of [18] for the DNA dataset.  ...  Convexity Measures A shape S is said to be convex if it has the following property: If points p, q ∈ R belong to S then all points from the line segment [pq] belong to S as well.  ... 
doi:10.7155/jgaa.00364 fatcat:4u5qdvj4anbzdjth64xz353uzy

On the Shortest Separating Cycle [article]

Adrian Dumitrescu
2019 arXiv   pre-print
In this regard, we prove a lemma on convex polygon approximation that is of independent interest.  ...  (III) Given a set of n point pairs in convex position in the plane, we show that a (1+ε)-approximation of a shortest separating cycle can be computed in time n^O(ε^-1/2).  ...  The author is grateful to an anonymous reviewer for his careful reading of the manuscript and pertinent remarks.  ... 
arXiv:1912.01541v1 fatcat:2s76gps46jbxfmnpciidzadyxa
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