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Testing Convexity Properties of Tree Colorings
2009
Algorithmica
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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]
STACS 2007
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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
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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]
2013
Lecture Notes in Computer Science
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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
1989
Discrete & Computational Geometry
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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
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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
2012
Discrete Applied Mathematics
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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]
2008
Lecture Notes in Computer Science
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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
2003
The Visual Computer
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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
2016
Mathematical programming
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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]
2011
arXiv
pre-print
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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
2012
Algorithms for Molecular Biology
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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
2015
Discrete & Computational Geometry
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2010 pre-print arXiv:1005.1721v1 fatcat:fi22m2gfajcavbb7nngzwir2su
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
2015
Journal of Graph Algorithms and Applications
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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]
2019
arXiv
pre-print
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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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