Let T be a weighted tree with n numbered leaves and let D = (D (i, j))i, j be its distance matrix, so D (i, j) is the distance between the leaves i and j. If m is an integer satisfying 2 ≤ m ≤ n, we prove a tropical formula to compute the m-dissimilarity map of T (i.e. the weights of the subtrees of T with m leaves), given D. For m = 3, we present a tropical description of the set of m-dissimilarity maps of trees. For m = 4, a partial result is given.

Bocci, C., & Cools, F. (2009). A tropical interpretation of m-dissimilarity maps. APPLIED MATHEMATICS AND COMPUTATION, 212(2), 349-356 [10.1016/j.amc.2009.02.031].

A tropical interpretation of m-dissimilarity maps

BOCCI, CRISTIANO;
2009

Abstract

Let T be a weighted tree with n numbered leaves and let D = (D (i, j))i, j be its distance matrix, so D (i, j) is the distance between the leaves i and j. If m is an integer satisfying 2 ≤ m ≤ n, we prove a tropical formula to compute the m-dissimilarity map of T (i.e. the weights of the subtrees of T with m leaves), given D. For m = 3, we present a tropical description of the set of m-dissimilarity maps of trees. For m = 4, a partial result is given.
File in questo prodotto:
File Dimensione Formato  
Bocci-Cools.pdf

non disponibili

Tipologia: Post-print
Licenza: NON PUBBLICO - Accesso privato/ristretto
Dimensione 201.39 kB
Formato Adobe PDF
201.39 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11365/21087
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo