Related papers: Computing Exact Distances in the Congested Clique
We give new, improved bounds for approximating the sparsest cut value or in other words the conductance $\phi$ of a graph in the CONGEST model. As our main result, we present an algorithm running in $O(\log^2 n/\phi)$ rounds in which every…
The importance of classifying connections in large graphs has been the motivation for a rich line of work on distributed subgraph finding that has led to exciting recent breakthroughs. A crucial aspect that remained open was whether…
Much progress has recently been made in understanding the complexity landscape of subgraph finding problems in the CONGEST model of distributed computing. However, so far, very few tight bounds are known in this area. For triangle (i.e.,…
Counting the number of triangles in a graph has many important applications in network analysis. Several frequently computed metrics like the clustering coefficient and the transitivity ratio need to count the number of triangles in the…
Round complexity is an extensively studied metric of distributed algorithms. In contrast, our knowledge of the \emph{message complexity} of distributed computing problems and its relationship (if any) with round complexity is still quite…
The all pairs shortest path problem is a fundamental optimization problem in graph theory. We deal with re-calculating the all-pairs shortest path (APSP) matrix after a minor modification of a weighted dense graph, e.g., adding a node,…
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…
We consider the quantum time complexity of the all pairs shortest paths (APSP) problem and some of its variants. The trivial classical algorithm for APSP and most all pairs path problems runs in $O(n^3)$ time, while the trivial algorithm in…
In a sequence of recent results (PODC 2015 and PODC 2016), the running time of the fastest algorithm for the \emph{minimum spanning tree (MST)} problem in the \emph{Congested Clique} model was first improved to $O(\log \log \log n)$ from…
We present near-optimal algorithms for detecting small vertex cuts in the CONGEST model of distributed computing. Despite extensive research in this area, our understanding of the vertex connectivity of a graph is still incomplete,…
Given a directed weighted graph $G=(V,E)$ undergoing vertex insertions \emph{and} deletions, the All-Pairs Shortest Paths (APSP) problem asks to maintain a data structure that processes updates efficiently and returns after each update the…
It is known that a better than $2$-approximation algorithm for the girth in dense directed unweighted graphs needs $n^{3-o(1)}$ time unless one uses fast matrix multiplication. Meanwhile, the best known approximation factor for a…
Identifying the connected components of a graph, apart from being a fundamental problem with countless applications, is a key primitive for many other algorithms. In this paper, we consider this problem in parallel settings. Particularly,…
We present simple deterministic algorithms for subgraph finding and enumeration in the broadcast CONGEST model of distributed computation: -- For any constant $k$, detecting $k$-paths and trees on $k$ nodes can be done in $O(1)$ rounds. --…
We consider the problem of approximate counting of triangles and longer fixed length cycles in directed graphs. For triangles, T\v{e}tek [ICALP'22] gave an algorithm that returns a $(1 \pm \eps)$-approximation in…
We consider the directed minimum weight cycle problem in the fully dynamic setting. To the best of our knowledge, so far no fully dynamic algorithms have been designed specifically for the minimum weight cycle problem in general digraphs.…
Computing shortest paths is one of the central problems in the theory of distributed computing. For the last few years, substantial progress has been made on the approximate single source shortest paths problem, culminating in an algorithm…
We present an algorithm that computes the girth of the intersection graph of $n$ given line segments in the plane in $O(n^{1.483})$ expected time. This is the first such algorithm with $O(n^{3/2-\varepsilon})$ running time for a positive…
We give a simple deterministic constant-round algorithm in the congested clique model for reducing the number of edges in a graph to $n^{1+\varepsilon}$ while preserving the minimum spanning forest, where $\varepsilon > 0$ is any constant.…
We consider the standard message passing model; we assume the system is fully synchronous: all processes start at the same time and time proceeds in synchronised rounds. In each round each vertex can transmit a different message of size…