Related papers: Dynamic constant time parallel graph algorithms wi…
We present the first work-optimal polylogarithmic-depth parallel algorithm for the minimum cut problem on non-sparse graphs. For $m\geq n^{1+\epsilon}$ for any constant $\epsilon>0$, our algorithm requires $O(m \log n)$ work and $O(\log^3…
Graph clustering has many important applications in computing, but due to growing sizes of graphs, even traditionally fast clustering methods such as spectral partitioning can be computationally expensive for real-world graphs of interest.…
Petersen's theorem, one of the earliest results in graph theory, states that any bridgeless cubic multigraph contains a perfect matching. While the original proof was neither constructive nor algorithmic, Biedl, Bose, Demaine, and Lubiw [J.…
Many statistical learning problems can be posed as minimization of a sum of two convex functions, one typically a composition of non-smooth and linear functions. Examples include regression under structured sparsity assumptions. Popular…
We present new approaches to constructing graph sparsifiers --- weighted subgraphs for which every cut has the same value as the original graph, up to a factor of $(1 \pm \epsilon)$. Our first approach independently samples each edge $uv$…
We present an efficient distributed memory parallel algorithm for computing connected components in undirected graphs based on Shiloach-Vishkin's PRAM approach. We discuss multiple optimization techniques that reduce communication volume as…
Given a large data graph, trimming techniques can reduce the search space by removing vertices without outgoing edges. One application is to speed up the parallel decomposition of graphs into strongly connected components (SCC…
Control parallelism and data parallelism is mostly reasoned and optimized as separate functions. Because of this, workloads that are irregular, fine-grain and dynamic such as dynamic graph processing become very hard to scale. An…
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 provide a framework for the design and analysis of dynamic programming algorithms for surface-embedded graphs on n vertices and branchwidth at most k. Our technique applies to general families of problems where standard dynamic…
Real-world graphs, such as social networks, financial transactions, and recommendation systems, often demonstrate dynamic behavior. This phenomenon, known as graph stream, involves the dynamic changes of nodes and the emergence and…
We present a fully dynamic algorithm for the recognition of proper circular-arc (PCA) graphs. The allowed operations on the graph involve the insertion and removal of vertices (together with its incident edges) or edges. Edge operations…
This paper considers the problem of distributed optimization over time-varying graphs. For the case of undirected graphs, we introduce a distributed algorithm, referred to as DIGing, based on a combination of a distributed inexact gradient…
Recent spectral graph sparsification research allows constructing nearly-linear-sized subgraphs that can well preserve the spectral (structural) properties of the original graph, such as the first few eigenvalues and eigenvectors of the…
We present a new approach for solving (minimum disagreement) correlation clustering that results in sublinear algorithms with highly efficient time and space complexity for this problem. In particular, we obtain the following algorithms for…
We address the problem of testing whether a given dynamic graph is temporally connected, {\it i.e} a temporal path (also called a {\em journey}) exists between all pairs of vertices. We consider a discrete version of the problem, where the…
Building on previous work by Cameron et al. in [3], we give a recurrence for computing the number of acyclic orientations of complete $k$-partite graphs, which can be implemented to obtain a dynamic programming algorithm running in time…
We consider the problem of computing compact routing tables for a (weighted) planar graph $G:= (V, E,w)$ in the PRAM, CONGEST, and the novel HYBRID communication model. We present algorithms with polylogarithmic work and communication that…
In this paper, we initiate the study of the dynamic maintenance of $2$-edge-connectivity relationships in directed graphs. We present an algorithm that can update the $2$-edge-connected blocks of a directed graph with $n$ vertices through a…
We present linear time {\it in-place} algorithms for several basic and fundamental graph problems including the well-known graph search methods (like depth-first search, breadth-first search, maximum cardinality search), connectivity…