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We consider the {\em mobile facility location} (\mfl) problem. We are given a set of facilities and clients located in a common metric space. The goal is to move each facility from its initial location to a destination and assign each…
Self-similarity of random trees is related to the operation of pruning. Pruning $R$ cuts the leaves and their parental edges and removes the resulting chains of degree-two nodes from a finite tree. A Horton-Strahler order of a vertex $v$…
We consider an information dissemination problem where the root of an undirected graph constantly updates its information. The goal is to keep every other node in the graph about the root as freshly informed as possible. Our synchronous…
We present a technique that allows for improving on some relative greedy procedures by well-chosen (non-oblivious) local search algorithms. Relative greedy procedures are a particular type of greedy algorithm that start with a simple,…
The recursive and hierarchical structure of full rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. In most of these cases, the full rooted tree is…
We introduce Sequential Probability Ratio Bisection (SPRB), a novel stochastic approximation algorithm that adapts to the local behavior of the (regression) function of interest around its root. We establish theoretical guarantees for…
While obtaining optimal algorithms for the most important problems in the LOCAL model has been one of the central goals in the area of distributed algorithms since its infancy, tight complexity bounds are elusive for many problems even when…
This paper extends the study of fringe trees in random plane trees with a given degree statistic. While previous work established the asymptotic normality of the count of fringe trees isomorphic to a fixed tree, we investigate the case…
We resolve a long-standing open question, about the existence of a constant-factor approximation algorithm for the average-case \textsc{Decision Tree} problem with uniform probability distribution over the hypotheses. We answer the question…
In this paper we present a novel probabilistic sampling-based motion planning algorithm called the Fast Marching Tree algorithm (FMT*). The algorithm is specifically aimed at solving complex motion planning problems in high-dimensional…
We consider growing random recursive trees in random environment, in which at each step a new vertex is attached (by an edge of a random length) to an existing tree vertex according to a probability distribution that assigns the tree…
We consider the problem of detecting the source of a rumor which has spread in a network using only observations about which set of nodes are infected with the rumor and with no information as to \emph{when} these nodes became infected. In…
Tree search algorithms, such as branch-and-bound, are the most widely used tools for solving combinatorial and nonconvex problems. For example, they are the foremost method for solving (mixed) integer programs and constraint satisfaction…
Moss and Rabani[12] study constrained node-weighted Steiner tree problems with two independent weight values associated with each node, namely, cost and prize (or penalty). They give an O(log n)-approximation algorithm for the…
Research in reinforcement learning has produced algorithms for optimal decision making under uncertainty that fall within two main types. The first employs a Bayesian framework, where optimality improves with increased computational time.…
Treedepth is a central parameter to algorithmic graph theory. The current state-of-the-art in computing and approximating treedepth consists of a $2^{O(k^2)} n$-time exact algorithm and a polynomial-time $O(\text{OPT} \log^{3/2}…
This paper presents the first convergence result for random search algorithms to a subset of the Pareto set of given maximum size k with bounds on the approximation quality. The core of the algorithm is a new selection criterion based on a…
This article is studying the roots of the reliability polynomials of linear consecutive-\textit{k}-out-of-\textit{n}:\textit{F} systems. We are able to prove that these roots are unbounded in the complex plane, for any fixed $k\ge2$. In the…
We study two models of growing recursive trees. For both models, initially the tree only contains one vertex $u_1$ and at each time $n\geq 2$ a new vertex $u_n$ is added to the tree and its parent is chosen randomly according to some rule.…
A chief problem in phylogenetics and database theory is the computation of a maximum consistent tree from a set of rooted or unrooted trees. A standard input are triplets, rooted binary trees on three leaves, or quartets, unrooted binary…