TAILIEUCHUNG - Báo cáo toán học: "haracterizing Cell-Decomposable Metrics"

Tuyển tập các báo cáo nghiên cứu khoa học về toán học trên tạp chí toán học quốc tế đề tài: Characterizing Cell-Decomposable Metrics. | Characterizing Cell-Decomposable Metrics Katharina T. Huber School of Computing Sciences University of East Anglia Norwich NR4 7TJ Uk Vincent Moulton School of Computing Sciences University of East Anglia Norwich NR4 7TJ Uk Jacobus Koolen Department of Mathematics POSTECH Pohang South Korea koolen@ Andreas Spillner School of Computing Sciences University of East Anglia Norwich NR4 7TJ Uk aspillner@ Submitted Aug 14 2007 Accepted Mar 6 2008 Published Mar 20 2008 Mathematics Subject Classifications 54E35 05C12 Abstract To a finite metric space X d one can associate the so called tight-span T d of d that is a canonical metric space T d d1 into which X d isometrically embeds and which may be thought of as the abstract convex hull of X d . Amongst other applications the tight-span of a finite metric space has been used to decompose and classify finite metrics to solve instances of the server and multicommodity flow problems and to perform evolutionary analyses of molecular data. To better understand the structure of T d d1 the concept of a cell-decomposable metric was recently introduced a metric whose associated tight-span can be decomposed into simpler tight-spans. Here we show that cell-decomposable metrics and totally split-decomposable metrics a class of metrics commonly applied within phylogenetic analysis are one and the same thing and also provide some additional characterizations of such metrics. 1 Introduction In this note X d denotes a finite metric space that is a finite set X together with a metric or function d X X X R 0 such that d x x 0 d x y d y x and d x z d x y d y z hold for all x y z 2 X. The tight-span T d of d 6 is the polytopal complex consisting of the bounded faces or cells of the polyhedron P d f 2 RX f x f y d x y for all x y 2 X THE ELECTRONIC JOURNAL OF COMBINATORICS 15 2008 N7 1 see Section 2 for the definition of a polyhedral complex and related concepts

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