Related papers: Parallel Minimum Cuts in $O(m \log^2(n))$ Work and…
This paper considers the \textit{minimum spanning tree (MST)} problem in the Congested Clique model and presents an algorithm that runs in $O(\log \log \log n)$ rounds, with high probability. Prior to this, the fastest MST algorithm in this…
Dynamic trees are a well-studied and fundamental building block of dynamic graph algorithms dating back to the seminal work of Sleator and Tarjan [STOC'81, (1981), pp. 114-122]. The problem is to maintain a tree subject to online edge…
We present fast algorithms for approximate shortest paths in the massively parallel computation (MPC) model. We provide randomized algorithms that take $poly(\log{\log{n}})$ rounds in the near-linear memory MPC model. Our results are for…
We present a deterministic O(n log log n) time algorithm for finding shortest cycles and minimum cuts in planar graphs. The algorithm improves the previously known fastest algorithm by Italiano et al. in STOC'11 by a factor of log n. This…
We study polynomial-time approximation algorithms for (edge/vertex) Sparsest Cut and Small Set Expansion in terms of $k$, the number of edges or vertices cut in the optimal solution. Our main results are $\mathcal{O}(\text{polylog}\,…
Hypergraph clustering is a basic algorithmic primitive for analyzing complex datasets and systems characterized by multiway interactions, such as group email conversations, groups of co-purchased retail products, and co-authorship data.…
We present a parallel algorithm for computing the minimum s-t cut in structured 3-dimensional proper order graphs arising from image segmentation problems. Proper order graphs are multi-column structures where vertices are arranged in…
This paper presents new deterministic and distributed low-diameter decomposition algorithms for weighted graphs. In particular, we show that if one can efficiently compute approximate distances in a parallel or a distributed setting, one…
We show that a simple algorithm for computing a matching on a graph runs in a logarithmic number of phases incurring work linear in the input size. The algorithm can be adapted to provide efficient algorithms in several models of…
Let $G$ be an $n$-node simple directed planar graph with nonnegative edge weights. We study the fundamental problems of computing (1) a global cut of $G$ with minimum weight and (2) a~cycle of $G$ with minimum weight. The best previously…
We present a parallel version of the cut-pursuit algorithm for minimizing functionals involving the graph total variation. We show that the decomposition of the iterate into constant connected components, which is at the center of this…
A low out-degree orientation directs each edge of an undirected graph with the goal of minimizing the maximum out-degree of a vertex. In the parallel batch-dynamic setting, one can insert or delete batches of edges, and the goal is to…
Minimum Spanning Tree (MST) is an important graph algorithm that has wide ranging applications in the areas of computer networks, VLSI routing, wireless communications among others. Today virtually every computer is built out of multi-core…
The nni-distance is a well-known distance measure for phylogenetic trees. We construct an efficient parallel approximation algorithm for the nni-distance in the CRCW-PRAM model running in O(log n) time on O(n) processors. Given two…
We study the problem of computing a minimum cut in a simple, undirected graph and give a deterministic $O(m \log^2 n \log\log^2 n)$ time algorithm. This improves both on the best previously known deterministic running time of $O(m \log^{12}…
We consider the problem of finding a minimum cut of a weighted graph presented as a single-pass stream. While graph sparsification in streams has been intensively studied, the specific application of finding minimum cuts in streams is less…
In this short note, we give a novel algorithm for $O(1)$ round triangle counting in bounded arboricity graphs. Counting triangles in $O(1)$ rounds (exactly) is listed as one of the interesting remaining open problems in the recent survey of…
This paper ties the line of work on algorithms that find an O(sqrt(log(n)))-approximation to the sparsest cut together with the line of work on algorithms that run in sub-quadratic time by using only single-commodity flows. We present an…
We use exponential start time clustering to design faster and more work-efficient parallel graph algorithms involving distances. Previous algorithms usually rely on graph decomposition routines with strict restrictions on the diameters of…
We present an in-place algorithm for the partition problem that has linear work and polylogarithmic span. The algorithm uses only exclusive read/write shared variables, and can be implemented using parallel-for-loops without any additional…