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Testing Convexity Properties of Tree Colorings

2009
*
Algorithmica
*

We give a 1-sided, non-adaptive, distribution-free -

doi:10.1007/s00453-009-9368-2
fatcat:pmm3xzizb5bejgc53g45gre4xu
*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. ...##
###
Testing Convexity Properties of Tree Colorings
[chapter]

*
STACS 2007
*

We give a 1-sided, non-adaptive, distribution-free -

doi:10.1007/978-3-540-70918-3_10
dblp:conf/stacs/FischerY07
fatcat:ljfvxcapand3tamitx6tjfs2iy
*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. ...##
###
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. ...##
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Point-Set Embeddability of 2-Colored Trees
[chapter]

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. ...

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

1989
*
Discrete & Computational Geometry
*

We present an algorithm for computing certain kinds

doi:10.1007/bf02187749
fatcat:imdybpi2lfh65izvvqu5woeneu
*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. ...##
###
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

2012
*
Discrete Applied Mathematics
*

A

doi:10.1016/j.dam.2011.09.022
fatcat:g2wesaystjdbppt4dxvsd4u4ca
*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. ...##
###
The Complexity of Minimum Convex Coloring
[chapter]

2008
*
Lecture Notes in Computer Science
*

A

doi:10.1007/978-3-540-92182-0_5
fatcat:ttifb5jzsvdmph2q3fdlf7l6cu
*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. ...##
###
Convex contouring of volumetric data

2003
*
The Visual Computer
*

Using the same technique, we can perform fast, crack-free multi-resolution contouring on nested grids

doi:10.1007/s00371-003-0216-0
fatcat:ocwagabblnfmlm5m3jghnn67ua
*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*. ...##
###
An extended formulation of the convex recoloring problem on a tree

2016
*
Mathematical programming
*

We introduce a strong extended formulation

doi:10.1007/s10107-016-1094-3
fatcat:3yotlteogjbixehzcfchuuo2ty
*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. ...##
###
Reconciling taxonomy and phylogenetic inference: formalism and algorithms for describing discord and inferring taxonomic roots
[article]

2011
*
arXiv
*
pre-print

Although taxonomy is often used informally to evaluate the results

arXiv:1109.5423v2
fatcat:wnuwxlelafaavd4z5zbuwx6gnu
*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. ...##
###
Reconciling taxonomy and phylogenetic inference: formalism and algorithms for describing discord and inferring taxonomic roots

2012
*
Algorithms for Molecular Biology
*

Although taxonomy is often used informally to evaluate the results

doi:10.1186/1748-7188-7-8
pmid:22549005
pmcid:PMC3384453
fatcat:ebrn4y2yv5dolal6vmfkv4yle4
*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. ...##
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Ramified Rectilinear Polygons: Coordinatization by Dendrons

2015
*
Discrete & Computational Geometry
*

The rectangular cell complexes that share this same embedding

doi:10.1007/s00454-015-9743-5
fatcat:yk7svrt4azarlmu5faonckwu2e
*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*. ...##
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MapSets: Visualizing Embedded and Clustered Graphs

2015
*
Journal of Graph Algorithms and Applications
*

The proposed method relies on a theoretically sound geometric algorithm which guarantees the contiguity and disjointness

doi:10.7155/jgaa.00364
fatcat:4u5qdvj4anbzdjth64xz353uzy
*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. ...##
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On the Shortest Separating Cycle
[article]

2019
*
arXiv
*
pre-print

In this regard, we prove a lemma on

arXiv:1912.01541v1
fatcat:2s76gps46jbxfmnpciidzadyxa
*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. ...
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