منابع مشابه
Subdominant matroid ultrametrics
Given a matroid M on the ground set E, the Bergman fan B̃(M), or space of M -ultrametrics, is a polyhedral complex in RE which arises in several different areas, such as tropical algebraic geometry, dynamical systems, and phylogenetics. Motivated by the phylogenetic situation, we study the following problem: Given a point ω in RE , we wish to find an M -ultrametric which is closest to it in the ...
متن کاملPlanar Ultrametrics for Image Segmentation
We study the problem of hierarchical clustering on planar graphs. We formulate this in terms of finding the closest ultrametric to a specified set of distances and solve it using an LP relaxation that leverages minimum cost perfect matching as a subroutine to efficiently explore the space of planar partitions. We apply our algorithm to the problem of hierarchical image segmentation.
متن کاملLow dimensional embeddings of ultrametrics
In this note we show that every n-point ultrametric embeds with constant distortion in l O(logn) p for every ∞ ≥ p ≥ 1. More precisely, we consider a special type of ultrametric with hierarchical structure called a k-hierarchically well-separated tree (k-HST). We show that any k-HST can be embedded with distortion at most 1 + O(1/k) in l O(k2 logn) p . These facts have implications to embedding...
متن کاملTrees, Ultrametrics, and Noncommutative Geometry
Noncommutative geometry is used to study the local geometry of ultrametric spaces and the geometry of trees at infinity. Connes’s example of the noncommutative space of Penrose tilings is interpreted as a non-Hausdorff orbit space of a compact, ultrametric space under the action of its local isometry group. This is generalized to compact, locally rigid, ultrametric spaces. The local isometry ty...
متن کاملModeling Timed Concurrent Systems using Generalized Ultrametrics
Timed concurrent systems are used in concurrent and distributed real-time software, modeling of hybrid systems, design of hardware systems (using hardware description languages), discrete-event simulation, and modeling of communication networks. They consist of concurrent components that communicate using timed signals, which are sets of (semantically) time-stamped events. The denotational sema...
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ژورنال
عنوان ژورنال: Annals of Combinatorics
سال: 2005
ISSN: 0218-0006,0219-3094
DOI: 10.1007/s00026-004-0227-1