相关论文: Tight Analysis of Randomized Greedy MIS

We propose distributed algorithms for two well-established problems that operate efficiently under extremely harsh conditions. Our algorithms achieve state-of-the-art performance in a simple and novel way. Our algorithm for maximal…

$\newcommand{\eps}{\varepsilon}$ In this paper, we consider two important problems defined on finite metric spaces, and provide efficient new algorithms and approximation schemes for these problems on inputs given as graph shortest path…

Randomized parallel algorithms for many fundamental problems achieve optimal linear work in expectation, but upgrading this guarantee to hold with high probability (whp) remains a recurring theoretical challenge. In this paper, we address…

In the $d$-Scattered Set problem we are asked to select at least $k$ vertices of a given graph, so that the distance between any pair is at least $d$. We study the problem's (in-)approximability and offer improvements and extensions of…

Identifying the connected components of a graph, apart from being a fundamental problem with countless applications, is a key primitive for many other algorithms. In this paper, we consider this problem in parallel settings. Particularly,…

We present a randomized Local Computation Algorithm (LCA) with query complexity $poly(\Delta) \cdot \log n$ for the Maximal Independent Set (MIS) problem. That is, the algorithm determines whether each node is in the computed MIS or not…

Centrality measures, quantifying the importance of vertices or edges, play a fundamental role in network analysis. To date, triggered by some positive approximability results, a large body of work has been devoted to studying centrality…

Greedy algorithms have been successfully analyzed and applied in training neural networks for solving variational problems, ensuring guaranteed convergence orders. In this paper, we extend the analysis of the orthogonal greedy algorithm…

In the past years, many quantum algorithms have been proposed to tackle hard combinatorial problems. These algorithms, which have been studied in depth in complexity theory, are at the heart of many industrial applications. In particular,…

The notion of {\em recoverable value} was advocated in work of Feige, Immorlica, Mirrokni and Nazerzadeh [Approx 2009] as a measure of quality for approximation algorithms. There this concept was applied to facility location problems. In…

Centrality measures characterize important nodes in networks. Efficiently computing such nodes has received a lot of attention. When considering the generalization of computing central groups of nodes, challenging optimization problems…

In the distributed backup-placement problem each node of a network has to select one neighbor, such that the maximum number of nodes that make the same selection is minimized. This is a natural relaxation of the perfect matching problem, in…

Given a graph, finding the distance-2 maximal independent set (MIS-2) of the vertices is a problem that is useful in several contexts such as algebraic multigrid coarsening or multilevel graph partitioning. Such multilevel methods rely on…

We bound the performance guarantees that follow from Tur\'an-like bounds for unweighted and weighted independent sets in bounded-degree graphs. In particular, a randomized approach of Boppana forms a simple 1-round distributed algorithm, as…

Finding locally optimal solutions for max-cut and max-$k$-cut are well-known PLS-complete problems. An instinctive approach to finding such a locally optimum solution is the FLIP method. Even though FLIP requires exponential time in…

We study the online load balancing problem on unrelated machines, with the objective of minimizing the square of the $\ell_2$ norm of the loads on the machines. The greedy algorithm of Awerbuch et al. (STOC'95) is optimal for deterministic…

We study parallel algorithms for the classical balls-into-bins problem, in which $m$ balls acting in parallel as separate agents are placed into $n$ bins. Algorithms operate in synchronous rounds, in each of which balls and bins exchange…

Maximum Inner Product Search (MIPS) is an important task in many machine learning applications such as the prediction phase of a low-rank matrix factorization model for a recommender system. There have been some works on how to perform MIPS…

We study the problem of computing approximate minimum edge cuts by distributed algorithms. We use a standard synchronous message passing model where in each round, $O(\log n)$ bits can be transmitted over each edge (a.k.a. the CONGEST…

Starting from a complete graph on $n$ vertices, repeatedly delete the edges of a uniformly chosen triangle. This stochastic process terminates once it arrives at a triangle-free graph, and the fundamental question is to estimate the final…