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In this paper, we focus on computing local minimizers of a multivariate polynomial optimization problem under certain genericity conditions. By using a technique in computer algebra and the second-order optimality condition, we provide a…
The distributed coloring problem is at the core of the area of distributed graph algorithms and it is a problem that has seen tremendous progress over the last few years. Much of the remarkable recent progress on deterministic distributed…
This text provides an introduction to distributed local algorithms -- an area at the intersection of theoretical computer science and discrete mathematics. We collect recent results in the area and demonstrate how they lead to a clean…
In this work we study local computation with advice: the goal is to solve a graph problem $\Pi$ with a distributed algorithm in $T(\Delta)$ communication rounds, for some function $T$ that only depends on the maximum degree $\Delta$ of the…
This paper introduces a new combinatorial framework for modeling the growth of binary trees through a discrete evolution process that incorporates a growing rule and an extinction rule. Building upon the theory of increasingly labeled…
We define a search problem on trees that closely captures the backtracking behavior of all current practical graph isomorphism algorithms. Given two trees with colored leaves, the goal is to find two leaves of matching color, one in each of…
In this paper, we study arbitrary infinite binary information systems each of which consists of an infinite set called universe and an infinite set of two-valued functions (attributes) defined on the universe. We consider the notion of a…
The Minimum Dominating Set (MDS) problem is one of the most fundamental and challenging problems in distributed computing. While it is well-known that minimum dominating sets cannot be approximated locally on general graphs, over the last…
An archetypal problem discussed in computer science is the problem of searching for a given number in a given set of numbers. Other than sequential search, the classic solution is to sort the list of numbers and then apply binary search.…
By prior work, there is a distributed algorithm that finds a maximal fractional matching (maximal edge packing) in $O(\Delta)$ rounds, where $\Delta$ is the maximum degree of the graph. We show that this is optimal: there is no distributed…
The Maximal Independent Set (MIS) problem is one of the basics in the study of locality in distributed graph algorithms. This paper presents an extremely simple randomized algorithm providing a near-optimal local complexity for this…
We prove lower bounds of order $n\log n$ for both the problem to multiply polynomials of degree $n$, and to divide polynomials with remainder, in the model of bounded coefficient arithmetic circuits over the complex numbers. These lower…
We study restricted computation models related to the Tree Evaluation Problem}. The TEP was introduced in earlier work as a simple candidate for the (*very*) long term goal of separating L and LogDCFL. The input to the problem is a rooted,…
This paper improves and in two cases nearly settles, up to logarithmically lower-order factors, the deterministic complexity of some of the most central problems in distributed graph algorithms, which have been studied for over three…
The degree splitting problem requires coloring the edges of a graph red or blue such that each node has almost the same number of edges in each color, up to a small additive discrepancy. The directed variant of the problem requires…
The problem of coloring the edges of an $n$-node graph of maximum degree $\Delta$ with $2\Delta - 1$ colors is one of the key symmetry breaking problems in the area of distributed graph algorithms. While there has been a lot of progress…
This paper addresses the cornerstone family of \emph{local problems} in distributed computing, and investigates the curious gap between randomized and deterministic solutions under bandwidth restrictions. Our main contribution is in…
Tree-based methods are powerful nonparametric techniques in statistics and machine learning. However, their effectiveness, particularly in finite-sample settings, is not fully understood. Recent applications have revealed their surprising…
We study a model of random $\mathcal{R}$-enriched trees that is based on weights on the $\mathcal{R}$-structures and allows for a unified treatment of a large family of random discrete structures. We establish distributional limits…
We study the {edge-coloring} problem in the message-passing model of distributed computing. This is one of the most fundamental and well-studied problems in this area. Currently, the best-known deterministic algorithms for (2Delta…