Related papers: Faster generation of random spanning trees
Random diffusions are a popular tool in Monte-Carlo estimations, with well established algorithms such as Walk-on-Spheres (WoS) going back several decades. In this work, we introduce diffusion estimators for the problems of angular…
We study the problem of constructing universal Steiner trees for undirected graphs. Given a graph $G$ and a root node $r$, we seek a single spanning tree $T$ of minimum {\em stretch}, where the stretch of $T$ is defined to be the maximum…
Processing graphs with temporal information (the temporal graphs) has become increasingly important in the real world. In this paper, we study efficient solutions to temporal graph applications using new algorithms for Incremental Minimum…
Random graphs are a central element of the study of complex dynamical networks such as the internet, the brain, or socioeconomic phenomena. New methods to generate random graphs can spawn new applications and give insights into more…
We investigate the spectrum of the infinitesimal generator of the continuous time random walk on a randomly weighted oriented graph. This is the non-Hermitian random nxn matrix L defined by L(j,k)=X(j,k) if k<>j and…
Graph embedding, representing local and global neighborhood information by numerical vectors, is a crucial part of the mathematical modeling of a wide range of real-world systems. Among the embedding algorithms, random walk-based algorithms…
We consider the Backup Placement problem in networks in the $\mathcal{CONGEST}$ distributed setting. Given a network graph $G = (V,E)$, the goal of each vertex $v \in V$ is selecting a neighbor, such that the maximum number of vertices in…
In the design and analysis of political redistricting maps, it is often useful to be able to sample from the space of all partitions of the graph of census blocks into connected subgraphs of equal population. There are influential Markov…
Given a directed graph $G=(V,A)$, the Directed Maximum Leaf Spanning Tree problem asks to compute a directed spanning tree (i.e., an out-branching) with as many leaves as possible. By designing a Branch-and-Reduced algorithm combined with…
Computing a directed minimum spanning tree, called arborescence, is a fundamental algorithmic problem, although not as common as its undirected counterpart. In 1967, Edmonds discussed an elegant solution. It was refined to run in…
We derive an exact closed-form analytical expression for the distribution of the cover time for a random walk over an arbitrary graph. In special case, we derive simplified exact expressions for the distributions of cover time for a…
We consider the NP-hard problem of finding a spanning tree with a maximum number of internal vertices. This problem is a generalization of the famous Hamiltonian Path problem. Our dynamic-programming algorithms for general and…
Given access to the vertex set $V$ of a connected graph $G=(V,E)$ and an oracle that given two vertices $u,v\in V$, returns the shortest path distance between $u$ and $v$, how many queries are needed to reconstruct $E$? Firstly, we show…
We study \emph{local computation algorithms (LCAs)} for constructing spanning trees. In this setting, the goal is to locally determine, for each edge $ e \in E $, whether it belongs to a spanning tree $ T $ of the input graph $ G $, where $…
This paper presents a spanning tree-based genetic algorithm (GA) for the reconfiguration of electrical distribution systems with the objective of minimizing active power losses. Due to low voltage levels at distribution systems, power…
This study introduces an algorithm that generates undirected graphs with three main characteristics of real-world networks: scale-freeness, short distances between nodes (small-world phenomenon), and large clustering coefficients. The main…
Speculative generation has emerged as a promising technique to accelerate inference in large language models (LLMs) by leveraging parallelism to verify multiple draft tokens simultaneously. However, the fundamental limits on the achievable…
We give an efficient algorithm to generate a graph from a distribution $\epsilon$-close to $G(n,p)$, in the sense of total variation distance. In particular, if $p$ is represented with $O(\log n)$-bit accuracy, then, with high probability,…
We provide a rearrangement based algorithm for fast detection of subgraphs of $k$ vertices with long escape times for directed or undirected networks. Complementing other notions of densest subgraphs and graph cuts, our method is based on…
Let $G$ be a connected graph in which almost all vertices have linear degrees and let $T$ be a uniform spanning tree of $G$. For any fixed rooted tree $F$ of height $r$ we compute the asymptotic density of vertices $v$ for which the…