Related papers: A Practical Parallel Algorithm for Diameter Approx…
We develop a novel parallel decomposition strategy for unweighted, undirected graphs, based on growing disjoint connected clusters from batches of centers progressively selected from yet uncovered nodes. With respect to similar previous…
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…
Maximum weight matching is one of the most fundamental combinatorial optimization problems with a wide range of applications in data mining and bioinformatics. Developing distributed weighted matching algorithms is challenging due to the…
The Massive Parallel Computation (MPC) model is a theoretical framework for popular parallel and distributed platforms such as MapReduce, Hadoop, or Spark. We consider the task of computing a large matching or small vertex cover in this…
In this paper, we show new strongly polynomial work-depth tradeoffs for computing single-source shortest paths (SSSP) in non-negatively weighted directed graphs in parallel. Most importantly, we prove that directed SSSP can be solved within…
We show an improved parallel algorithm for decomposing an undirected unweighted graph into small diameter pieces with a small fraction of the edges in between. These decompositions form critical subroutines in a number of graph algorithms.…
We develop a new approach for distributed distance computation in planar graphs that is based on a variant of the metric compression problem recently introduced by Abboud et al. [SODA'18]. One of our key technical contributions is in…
As a measure of vertex importance according to the graph structure, PageRank has been widely applied in various fields. While many PageRank algorithms have been proposed in the past decades, few of them take into account whether the graph…
We design and implement an efficient parallel algorithm for finding a perfect matching in a weighted bipartite graph such that weights on the edges of the matching are large. This problem differs from the maximum weight matching problem,…
We propose a fast approximate algorithm for large graph matching. A new projected fixed-point method is defined and a new doubly stochastic projection is adopted to derive the algorithm. Previous graph matching algorithms suffer from high…
We present a new randomized algorithm for computing the diameter of a weighted directed graph. The algorithm runs in $\Ot(M^{\w/(\w+1)}n^{(\w^2+3)/(\w+1)})$ time, where $\w < 2.376$ is the exponent of fast matrix multiplication, $n$ is the…
We present a general method of designing fast approximation algorithms for cut-based minimization problems in undirected graphs. In particular, we develop a technique that given any such problem that can be approximated quickly on trees,…
Randomized parallel algorithms for many fundamental problems achieve optimal linear work in expectation, but upgrading this guarantee to hold with high probability (whp) remains a recurring theoretical challenge. In this paper, we address…
This paper gives poly-logarithmic-round, distributed D-approximation algorithms for covering problems with submodular cost and monotone covering constraints (Submodular-cost Covering). The approximation ratio D is the maximum number of…
We present a nearly linear work parallel algorithm for approximating the Held-Karp bound for the Metric TSP problem. Given an edge-weighted undirected graph $G=(V,E)$ on $m$ edges and $\epsilon>0$, it returns a $(1+\epsilon)$-approximation…
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…
The densest subgraph problem has received significant attention, both in theory and in practice, due to its applications in problems such as community detection, social network analysis, and spam detection. Due to the high cost of obtaining…
We describe approximation algorithms in Linial's classic LOCAL model of distributed computing to find maximum-weight matchings in a hypergraph of rank $r$. Our main result is a deterministic algorithm to generate a matching which is an…
In many models for large-scale computation, decomposition of the problem is key to efficient algorithms. For distance-related graph problems, it is often crucial that such a decomposition results in clusters of small diameter, while the…
More and more large data collections are gathered worldwide in various IT systems. Many of them possess the networked nature and need to be processed and analysed as graph structures. Due to their size they require very often usage of…