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» On Ultrametric Algorithmic Information
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SODA
2007
ACM
106views Algorithms» more  SODA 2007»
13 years 7 months ago
Embedding metrics into ultrametrics and graphs into spanning trees with constant average distortion
This paper addresses the basic question of how well can a tree approximate distances of a metric space or a graph. Given a graph, the problem of constructing a spanning tree in a ...
Ittai Abraham, Yair Bartal, Ofer Neiman
TALG
2008
81views more  TALG 2008»
13 years 6 months ago
Ordinal embeddings of minimum relaxation: General properties, trees, and ultrametrics
We introduce a new notion of embedding, called minimum-relaxation ordinal embedding, parallel to the standard notion of minimum-distortion (metric) embedding. In an ordinal embedd...
Noga Alon, Mihai Badoiu, Erik D. Demaine, Martin F...
COMPGEOM
2008
ACM
13 years 7 months ago
Circular partitions with applications to visualization and embeddings
We introduce a hierarchical partitioning scheme of the Euclidean plane, called circular partitions. Such a partition consists of a hierarchy of convex polygons, each having small ...
Krzysztof Onak, Anastasios Sidiropoulos
APPROX
2005
Springer
88views Algorithms» more  APPROX 2005»
13 years 11 months ago
Approximating the Best-Fit Tree Under Lp Norms
Abstract. We consider the problem of fitting an n × n distance matrix M by a tree metric T. We give a factor O(min{n1/p , (k log n)1/p }) approximation algorithm for finding the...
Boulos Harb, Sampath Kannan, Andrew McGregor
EOR
2006
110views more  EOR 2006»
13 years 6 months ago
Scatter search with path relinking for phylogenetic inference
We propose the use of scatter search with path relinking for the inference of phylogenetic trees. Solutions are here represented as trees whose leaves span the set of species unde...
Carlos Cotta