Related papers: Sandpile Prediction on Undirected Graphs
Finding dense subgraphs is a fundamental algorithmic tool in data mining, community detection, and clustering. In this problem, one aims to find an induced subgraph whose edge-to-vertex ratio is maximized. We study the directed case of this…
Sampling edges from a graph in sublinear time is a fundamental problem and a powerful subroutine for designing sublinear-time algorithms. Suppose we have access to the vertices of the graph and know a constant-factor approximation to the…
We analyze two algorithms for approximating the general optimal transport (OT) distance between two discrete distributions of size $n$, up to accuracy $\varepsilon$. For the first algorithm, which is based on the celebrated Sinkhorn's…
We present the first sublinear-in-$n$ round algorithm for sampling an approximately uniform spanning tree of an $n$-vertex graph in the CongestedClique model of distributed computing. In particular, our algorithm requires…
We define two general classes of nonabelian sandpile models on directed trees (or arborescences) as models of nonequilibrium statistical phenomena. These models have the property that sand grains can enter only through specified reservoirs,…
Depth first search (DFS) tree is a fundamental data structure for solving graph problems. The classical algorithm [SiComp74] for building a DFS tree requires $O(m+n)$ time for a given graph $G$ having $n$ vertices and $m$ edges. Recently,…
Spectral independence is a recently-developed framework for obtaining sharp bounds on the convergence time of the classical Glauber dynamics. This new framework has yielded optimal $O(n \log n)$ sampling algorithms on bounded-degree graphs…
Machine learning pipelines often rely on optimization procedures to make discrete decisions (e.g., sorting, picking closest neighbors, or shortest paths). Although these discrete decisions are easily computed, they break the…
Consider a generalization of the classical binary search problem in linearly sorted data to the graph-theoretic setting. The goal is to design an adaptive query algorithm, called a strategy, that identifies an initially unknown target…
This paper presents improved approximation algorithms for the problem of multiprocessor scheduling under uncertainty, or SUU, in which the execution of each job may fail probabilistically. This problem is motivated by the increasing use of…
We develop a new algorithmic technique that allows to transfer some constant time approximation algorithms for general graphs into random order streaming algorithms. We illustrate our technique by proving that in random order streams with…
Graph processing is used extensively in areas from social networking mining to web indexing. We demonstrate that the performance and dependability of such applications critically hinges on the graph data structure used, because a fixed,…
We propose two spectral algorithms for partitioning nodes in directed graphs respectively with a cyclic and an acyclic pattern of connection between groups of nodes. Our methods are based on the computation of extremal eigenvalues of the…
We introduce new data structures for answering connectivity queries in graphs subject to batched vertex failures. A deterministic structure processes a batch of $d\leq d_{\star}$ failed vertices in $\tilde{O}(d^3)$ time and thereafter…
We give improved algorithms for maintaining edge-orientations of a fully-dynamic graph, such that the out-degree of each vertex is bounded. On one hand, we show how to orient the edges such that the out-degree of each vertex is proportional…
In the abelian sandpile model, recurrent chip configurations are of interest as they are a natural choice of coset representatives under the quotient of the reduced Laplacian. We investigate graphs whose recurrent identities with respect to…
We study the abelian sandpile model on a random binary tree. Using a transfer matrix approach introduced by Dhar & Majumdar, we prove exponential decay of correlations, and in a small supercritical region (i.e., where the branching process…
We give a simple characterization of the functions that can be computed deterministically by anonymous processes in dynamic networks, depending on the number of leaders in the network. In addition, we provide efficient distributed…
We introduce and study numerically a directed two-dimensional sandpile automaton with probabilistic toppling (probability parameter p) which provides a good laboratory to study both self-organized criticality and the far-from-equilibrium…
We consider the observability model in networks with arbitrary topologies. We introduce a system of coupled nonlinear equations, valid under the locally tree-like ansatz, to describe the size of the largest observable cluster as a function…