Related papers: Dynamic constant time parallel graph algorithms wi…
With the proliferation of temporal graph data, there is a growing demand for analyzing information propagation patterns during graph evolution. Existing graph analysis systems, mostly based on static snapshots, struggle to effectively…
Graph sparsification serves as a foundation for many algorithms, such as approximation algorithms for graph cuts and Laplacian system solvers. As its natural generalization, hypergraph sparsification has recently gained increasing…
We address the problem of testing whether a dynamic graph is temporally connected, i.e. a temporal path ({\em journey}) exists between all pairs of vertices. We consider a discrete version of the problem, where the topology is given as an…
Consider two planar graphs which are subject to edge insertions and deletions. We show that whether the two graphs are isomorphic can be maintained with first-order logic formulas and auxiliary data of polynomial size. This places the…
Many modern parallel systems, such as MapReduce, Hadoop and Spark, can be modeled well by the MPC model. The MPC model captures well coarse-grained computation on large data --- data is distributed to processors, each of which has a…
In this paper, we present an on-line fully dynamic algorithm for maintaining strongly connected component of a directed graph in a shared memory architecture. The edges and vertices are added or deleted concurrently by fixed number of…
For any undirected and weighted graph $G=(V,E,w)$ with $n$ vertices and $m$ edges, we call a sparse subgraph $H$ of $G$, with proper reweighting of the edges, a $(1+\varepsilon)$-spectral sparsifier if \[…
We developed a flexible parallel algorithm for graph summarization based on vertex-centric programming and parameterized message passing. The base algorithm supports infinitely many structural graph summary models defined in a formal…
We propose an exact algorithm for solving the longest simple path problem between two given vertices in undirected weighted graphs. By using graph partitioning and dynamic programming, we obtain an algorithm that is significantly faster…
The notion of vertex sparsification is introduced in \cite{M}, where it was shown that for any graph $G = (V, E)$ and a subset of $k$ terminals $K \subset V$, there is a polynomial time algorithm to construct a graph $H = (K, E_H)$ on just…
Graph algorithms enormously contribute to the domains such as blockchains, social networks, biological networks, telecommunication networks, and several others. The ever-increasing demand of data-volume, as well as speed of such…
We give a quasipolynomial time algorithm for the graph matching problem (also known as noisy or robust graph isomorphism) on correlated random graphs. Specifically, for every $\gamma>0$, we give a $n^{O(\log n)}$ time algorithm that given a…
We initiate the study of graph algorithms in the streaming setting on massive distributed and parallel systems inspired by practical data processing systems. The objective is to design algorithms that can efficiently process evolving graphs…
A matching in a graph is a set of edges no two of which share a common vertex. A matching M is an induced matching if no edge connects two edges of M. The problem of finding a maximum induced matching is known to be NP-hard in general and…
Graph Convolutional Networks (GCNs) are extensively utilized for deep learning on graphs. The large data sizes of graphs and their vertex features make scalable training algorithms and distributed memory systems necessary. Since the…
We describe a synchronous distributed algorithm which identifies the edge-biconnected components of a connected network. It requires a leader, and uses messages of size O(log |V|). The main idea is to preorder a BFS spanning tree, and then…
We present a data structure that can maintain a simple planar graph under edge contractions in linear total time. The data structure supports adjacency queries and provides access to neighbor lists in $O(1)$ time. Moreover, it can report…
In this note, we revisit the rounding algorithm of Wajc. Wajc gave a fully-adaptive randomized algorithm that rounds a dynamic fractional matching in an unweighted bipartite graph to an integral matching of nearly the same value in…
Graph randomisation is a crucial task in the analysis and synthesis of networks. It is typically implemented as an edge switching process (ESMC) repeatedly swapping the nodes of random edge pairs while maintaining the degrees involved.…
We give an algorithm that decides whether the bipartite crossing number of a given graph is at most $k$. The running time of the algorithm is upper bounded by $2^{O(k)} + n^{O(1)}$, where $n$ is the number of vertices of the input graph,…