Related papers: Abstract Huffman Coding and PIFO Tree Embeddings
A widely used method for determining the similarity of two labeled trees is to compute a maximum agreement subtree of the two trees. Previous work on this similarity measure is only concerned with the comparison of labeled trees of two…
We consider the creation conditions of diverse hierarchical trees both analytically and numerically. A connection between the probabilities to create hierarchical levels and the probability to associate these levels into a united structure…
Algorithms for binary classification based on adaptive tree partitioning are formulated and analyzed for both their risk performance and their friendliness to numerical implementation. The algorithms can be viewed as generating a set…
A loss-less compression technique is proposed which uses a variable length Region formation technique to divide the input file into a number of variable length regions. Huffman codes are obtained for entire file after formation of regions.…
We study a class of combinatorial objects that we call "decorated trees". These consist of vertices, arrows and edges, where each edge is decorated by two integers (one near each of its endpoints), each arrow is decorated by an integer, and…
In this paper, we study the graph classification problem from the graph homomorphism perspective. We consider the homomorphisms from $F$ to $G$, where $G$ is a graph of interest (e.g. molecules or social networks) and $F$ belongs to some…
There is a deep connection between permutations and trees. Certain sub-structures of permutations, called sub-permutations, bijectively map to sub-trees of binary increasing trees. This opens a powerful tool set to study enumerative and…
Mining frequent tree patterns has many applications in different areas such as XML data, bioinformatics and World Wide Web. The crucial step in frequent pattern mining is frequency counting, which involves a matching operator to find…
We propose a flexible and multi-scale method for organizing, visualizing, and understanding datasets sampled from or near stratified spaces. The first part of the algorithm produces a cover tree using adaptive thresholds based on a…
In this paper, we investigate adaptive nonlinear regression and introduce tree based piecewise linear regression algorithms that are highly efficient and provide significantly improved performance with guaranteed upper bounds in an…
Forest automata (FA) have recently been proposed as a tool for shape analysis of complex heap structures. FA encode sets of tree decompositions of heap graphs in the form of tuples of tree automata. In order to allow for representing…
Given two messages - as linear sequences of letters, it is immediate to determine whether one can be transformed into the other by simple substitution cipher of the letters. On the other hand, if the letters are carried as labels on nodes…
A new Chase-type soft-decision decoding algorithm for Reed-Solomon codes is proposed, referred to as tree-based Chase-type algorithm}. The proposed tree-based Chase-type algorithm takes the set of all vectors as the set of testing patterns,…
We consider both analytically and numerically creation conditions of diverse hierarchical trees. A connection between the probabilities to create hierarchical levels and the probability to associate these levels into united structure is…
Loday and Ronco defined an interesting Hopf algebra structure on the linear span of the set of planar binary trees. They showed that the inclusion of the Hopf algebra of non-commutative symmetric functions in the Malvenuto-Reutenauer Hopf…
We discuss hamiltonian structures of the Gelfand-Dorfman complex of projectable vector fields and differential forms on a foliated manifold. Such a structure defines a Poisson structure on the algebra of foliated functions, and embeds the…
In this paper we offer a new perspective on the well established agglomerative clustering algorithm, focusing on recovery of hierarchical structure. We recommend a simple variant of the standard algorithm, in which clusters are merged by…
Fixed tree topologies are widely used in phylodynamic analyses to reduce computational burden, yet the consequences of this assumption remain insufficiently understood. Here, we systematically assess the impact of various fixed-topology…
We give correct explicit formulas for the probabilities of rooted binary trees and cladograms under Ford's $\alpha$-model.
Phylogenetic trees canonically arise as embeddings of phylogenetic networks. We recently showed that the problem of deciding if two phylogenetic networks embed the same sets of phylogenetic trees is computationally hard, \blue{in…