Related papers: Root finding algorithms and persistence of Jordan …
In this note we analyze the performance of a simple root-finding algorithm in uniform attachment trees. The leaf-stripping algorithm recursively removes all leaves of the tree for a carefully chosen number of rounds. We show that, with…
During the last decade, incremental sampling-based motion planning algorithms, such as the Rapidly-exploring Random Trees (RRTs) have been shown to work well in practice and to possess theoretical guarantees such as probabilistic…
We consider the following basic problem in phylogenetic tree construction. Let $\mathcal{P} = \{T_1, \ldots, T_k\}$ be a collection of rooted phylogenetic trees over various subsets of a set of species. The tree compatibility problem asks…
The Subtree Isomorphism problem asks whether a given tree is contained in another given tree. The problem is of fundamental importance and has been studied since the 1960s. For some variants, e.g., ordered trees, near-linear time algorithms…
We address the problem of building and maintaining distributed spanning trees in highly dynamic networks, in which topological events can occur at any time and any rate, and no stable periods can be assumed. In these harsh environments, we…
We study the use of sampling for efficiently mining the top-K frequent itemsets of cardinality at most w. To this purpose, we define an approximation to the top-K frequent itemsets to be a family of itemsets which includes (resp., excludes)…
We study structural properties of trees grown by preferential attachment. In this mechanism, nodes are added sequentially and attached to existing nodes at a rate that is strictly proportional to the degree. We classify nodes by their depth…
A uniform attachment tree is a random tree that is generated dynamically. Starting from a fixed "seed" tree, vertices are added sequentially by attaching each vertex to an existing vertex chosen uniformly at random. Upon observing a large…
A method to solve the problem f(x) = 0 efficiently on any n-dimensional domain Omega under very broad hypoteses is proposed. The position of the root of f, assumed unique, is found by computing the center of mass of an Omega-shaped object…
We study a natural analogue of Ulam's problem for random rooted trees distributed according to a Plancherel-type measure. This probability measure is closely related to the classical Plancherel measure on integer partitions. For a…
Kernels ensuing from tree ensembles such as random forest (RF) or gradient boosted trees (GBT), when used for kernel learning, have been shown to be competitive to their respective tree ensembles (particularly in higher dimensional…
We extend the results of B. Bollobas, O. Riordan, J. Spencer, G. Tusnady, and Mori. We consider a model of random tree growth, where at each time unit a new node is added and attached to an already existing node chosen at random. The…
In this paper we design and prove correct a fully dynamic distributed algorithm for maintaining an approximate Steiner tree that connects via a minimum-weight spanning tree a subset of nodes of a network (referred as Steiner members or…
In phylogenetics, a central problem is to infer the evolutionary relationships between a set of species $X$; these relationships are often depicted via a phylogenetic tree -- a tree having its leaves univocally labeled by elements of $X$…
We study a new notion of graph centrality based on absorbing random walks. Given a graph $G=(V,E)$ and a set of query nodes $Q\subseteq V$, we aim to identify the $k$ most central nodes in $G$ with respect to $Q$. Specifically, we consider…
We investigate Newton's method as a root finder for complex polynomials of arbitrary degree. While polynomial root finding continues to be one of the fundamental tasks of computing, with essential use in all areas of theoretical…
Decision Tree is a classic formulation of active learning: given $n$ hypotheses with nonnegative weights summing to 1 and a set of tests that each partition the hypotheses, output a decision tree using the provided tests that uniquely…
We deal with the problem of maintaining a shortest-path tree rooted at some process r in a network that may be disconnected after topological changes. The goal is then to maintain a shortest-path tree rooted at r in its connected component,…
We propose a simple generalization of standard and empirically successful decision tree learning algorithms such as ID3, C4.5, and CART. These algorithms, which have been central to machine learning for decades, are greedy in nature: they…
Let (X,d_X) be an n-point metric space. We show that there exists a distribution D over non-contractive embeddings into trees f:X-->T such that for every x in X, the expectation with respect to D of the maximum over y in X of the ratio…