Related papers: Average Size of a Suffix Tree for Markov Sources
Tries are among the most versatile and widely used data structures on words. In particular, they are used in fundamental sorting algorithms such as radix sort which we study in this paper. While the performance of radix sort and tries under…
Tree-based protocols are ubiquitous in distributed systems. They are flexible, they perform generally well, and, in static conditions, their analysis is mostly simple. Under churn, however, node joins and failures can have complex global…
We present an approach to email filtering based on the suffix tree data structure. A method for the scoring of emails using the suffix tree is developed and a number of scoring and score normalisation functions are tested. Our results show…
Starting from any graph on $\{1, \ldots, n\}$, consider the Markov chain where at each time-step a uniformly chosen vertex is disconnected from all of its neighbors and reconnected to another uniformly chosen vertex. This Markov chain has a…
Tries are among the most versatile and widely used data structures on words. They are pertinent to the (internal) structure of (stored) words and several splitting procedures used in diverse contexts ranging from document taxonomy to IP…
We prove an apparently novel concentration of measure result for Markov tree processes. The bound we derive reduces to the known bounds for Markov processes when the tree is a chain, thus strictly generalizing the known Markov process…
We study (plane) tree-valued Markov chains $(T_n,n \geq 1)$ with uniform backward dynamics and show that they can be obtained by sampling from a real tree. As non--plane trees, every such Markov chain is represented by a weighted real tree.…
Can we obtain a Brownian CRT of mass $1/2$ from a CRT of mass $1$ by cutting certain branches? In this paper, we will answer that question in the much more general setting of self-similar Markov trees. Self-similar Markov trees (ssMt) are…
We study the local limit of the fixed-point forest, a tree structure associated to a simple sorting algorithm on permutations. This local limit can be viewed as an infinite random tree that can be constructed from a Poisson point process…
Net-trees are a general purpose data structure for metric data that have been used to solve a wide range of algorithmic problems. We give a simple randomized algorithm to construct net-trees on doubling metrics using $O(n\log n)$ time in…
Many common sequential data sources, such as source code and natural language, have a natural tree-structured representation. These trees can be generated by fitting a sequence to a grammar, yielding a hierarchical ordering of the tokens in…
Most of the syntax-based metrics obtain the similarity by comparing the sub-structures extracted from the trees of hypothesis and reference. These sub-structures are defined by human and can't express all the information in the trees…
This paper is a variation on the uniform spanning tree theme. We use random spanning forests to solve the following problem: for a Markov process on a finite set of size $n$, find a probability law on the subsets of any given size $m \leq…
Recent work has proven the existence of extreme inbreeding in a European ancestry sample taken from the contemporary UK population \cite{nature_01}. This result brings our attention again to a math problem related to inbreeding family trees…
A fundamental algorithm for selecting ranks from a finite subset of an ordered set is Radix Selection. This algorithm requires the data to be given as strings of symbols over an ordered alphabet, e.g., binary expansions of real numbers. Its…
The reliability of a phylogenetic inference method from genomic sequence data is ensured by its statistical consistency. Bayesian inference methods produce a sample of phylogenetic trees from the posterior distribution given sequence data.…
Causal discovery algorithms typically recover causal graphs only up to their Markov equivalence classes unless additional parametric assumptions are made. The sizes of these equivalence classes reflect the limits of what can be learned…
We define some new sequences of recursively constructed random combinatorial trees, and show that, after properly rescaling graph distance and equipping the trees with the uniform measure on vertices, each sequence converges almost surely…
The syntactic structure of a sentence is often represented using syntactic dependency trees. The sum of the distances between syntactically related words has been in the limelight for the past decades. Research on dependency distances led…
The sizes of Markov equivalence classes of directed acyclic graphs play important roles in measuring the uncertainty and complexity in causal learning. A Markov equivalence class can be represented by an essential graph and its undirected…