Related papers: Faster Parallel Batch-Dynamic Algorithms for Low O…
One of the simplest problems on directed graphs is that of identifying the set of vertices reachable from a designated source vertex. This problem can be solved easily sequentially by performing a graph search, but efficient parallel…
We present the first parallel depth-first search algorithm for undirected graphs that has near-linear work and sublinear depth. Concretely, in any $n$-node $m$-edge undirected graph, our algorithm computes a DFS in $\tilde{O}(\sqrt{n})$…
We show how to find and efficiently maintain maximal k-edge-connected subgraphs in undirected graphs. In particular, we provide the following results. (1) A general framework for maintaining the maximal k-edge-connected subgraphs upon…
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…
We present the design and analysis of a near linear-work parallel algorithm for solving symmetric diagonally dominant (SDD) linear systems. On input of a SDD $n$-by-$n$ matrix $A$ with $m$ non-zero entries and a vector $b$, our algorithm…
For $n$-vertex $m$-edge graphs with integer polynomially-bounded costs and capacities, we provide a randomized parallel algorithm for the minimum cost flow problem with $\tilde O(m+n^ {1.5})$ work and $\tilde O(\sqrt{n})$ depth. On…
The core numbers of vertices in a graph are one of the most well-studied cohesive subgraph models because of the linear running time. In practice, many data graphs are dynamic graphs that are continuously changing by inserting or removing…
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,…
We present the first parallel batch-dynamic algorithm for maintaining a proper $(\Delta + 1)$-vertex coloring. Our approach builds on a new sequential dynamic algorithm inspired by the work of Bhattacharya et al. (SODA'18). The resulting…
The minimum degree algorithm is one of the most widely-used heuristics for reducing the cost of solving large sparse systems of linear equations. It has been studied for nearly half a century and has a rich history of bridging techniques…
We consider the question of orienting the edges in a graph $G$ such that every vertex has bounded out-degree. For graphs of arboricity $\alpha$, there is an orientation in which every vertex has out-degree at most $\alpha$ and, moreover,…
The subgradient method is one of the most fundamental algorithmic schemes for nonsmooth optimization. The existing complexity and convergence results for this method are mainly derived for Lipschitz continuous objective functions. In this…
We present a parallel algorithm for computing $(1+\epsilon)$-approximate mincost flow on an undirected graph with $m$ edges, where capacities and costs are assigned to both edges and vertices. Our algorithm achieves $\hat{O}(m)$ work and…
Zeroth-order optimization is the process of minimizing an objective $f(x)$, given oracle access to evaluations at adaptively chosen inputs $x$. In this paper, we present two simple yet powerful GradientLess Descent (GLD) algorithms that do…
We present a parallel algorithm for the $(1-\epsilon)$-approximate maximum flow problem in capacitated, undirected graphs with $n$ vertices and $m$ edges, achieving $O(\epsilon^{-3}\text{polylog} n)$ depth and $O(m \epsilon^{-3}…
One approach for reducing run time and improving efficiency of machine learning is to reduce the convergence rate of the optimization algorithm used. Shuffling is an algorithm technique that is widely used in machine learning, but it only…
We study the problem of finding and monitoring fixed-size subgraphs in a continually changing large-scale graph. We present the first approach that (i) performs worst-case optimal computation and communication, (ii) maintains a total memory…
We obtain better algorithms for computing more balanced orientations and degree splits in LOCAL. Important to our result is a connection to the hypergraph sinkless orientation problem [BMNSU, SODA'25] We design an algorithm of complexity…
Given a simple undirected graph $G$, an orientation of $G$ is to assign every edge of $G$ a direction. Borradaile et al gave a greedy algorithm SC-Path-Reversal (in polynomial time) which finds a strongly connected orientation that…
Despite there being significant work on developing spectral, and metric embedding based approximation algorithms for hypergraph generalizations of conductance, little is known regarding the approximability of hypergraph partitioning…