Finding the centrality measures of nodes in a graph is a problem of fundamental importance due to various applications from social networks, biological networks, and transportation networks. Given the large size of su...
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Finding the centrality measures of nodes in a graph is a problem of fundamental importance due to various applications from social networks, biological networks, and transportation networks. Given the large size of such graphs, it is natural to use parallelism as a recourse. Several studies show how to compute the various centrality measures of nodes in a graph on parallel architectures, including multi-core systems and GPUs. However, as these graphs evolve and change, it is pertinent to study how to update the centrality measures on changes to the underlying graph. In this article, we show novel parallel algorithms for updating the betweenness- and closeness-centrality values of nodes in a dynamicgraph. Our algorithms process a batch of updates in parallel by extending the approach of handling a single update for betweenness- and closeness-centrality. For the latter, we also introduce techniques based on traversals of the block-cut tree of a graph. Besides, our algorithms incorporate mechanisms to exploit the structural properties of graphs for enhanced performance. We implement our algorithms on two parallel architectures: an Intel 24-core CPU and an Nvidia Tesla V100 GPU. To the best of our knowledge, we are the first to show GPU algorithms for the above two problems. In addition, we conduct detailed experiments to study the impact of various parameters associated with our algorithms and their implementation. Our results on a collection of real-world graphs indicate that our algorithms achieve a significant speedup over corresponding state-of-the-art algorithms.
We give a fully dynamic (Las-Vegas style) algorithm with constant expected amortized time per update that maintains a proper (Delta+1)-vertex coloring of a graph with maximum degree at most Delta. This improves upon t...
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We give a fully dynamic (Las-Vegas style) algorithm with constant expected amortized time per update that maintains a proper (Delta+1)-vertex coloring of a graph with maximum degree at most Delta. This improves upon the previous O(log Delta)-time algorithm by Bhattacharya et al. (SODA 2018). Our algorithm uses an approach based on assigning random ranks to vertices and does not need to maintain a hierarchical graph decomposition. We show that our result does not only have optimal running time but is also optimal in the sense that already deciding whether a Delta-coloring exists in a dynamically changing graph with maximum degree at most Delta takes Omega(logn) time per operation.
Computing the winning set for Buchi objectives in alternating games on graphs is a central problem in computer aided verification with a large number of applications. The long standing best known upper bound for solvi...
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ISBN:
(纸本)9781611972108
Computing the winning set for Buchi objectives in alternating games on graphs is a central problem in computer aided verification with a large number of applications. The long standing best known upper bound for solving the problem is O{top}~(n·m), where n is the number of vertices and m is the number of edges in the graph. We are the first to break the O{top}~(n·m) boundary by presenting a new technique that reduces the running time to O(n~2). This bound also leads to O(n~2) time algorithms for computing the set of almost-sure winning vertices for Buchi objectives (1) in alternating games with probabilistic transitions (improving an earlier bound of {top}O(n·m)), (2) in concurrent graph games with constant actions (improving an earlier bound of O(n~3)), and (3) in Markov decision processes (improving for m ＞ n~(4/3) an earlier bound of O(min(m~(1.5),m· n~(2/3))). We also show that the same technique can be used to compute the maximal end-component decomposition of a graph in time O(n~2), which is an improvement over earlier bounds for m ＞ n~(4/3). Finally, we show how to maintain the winning set for Buchi objectives in alternating games under a sequence of edge insertions or a sequence of edge deletions in O(n) amortized time per operation. This is the first dynamic algorithm for this problem.
We consider the problem of maintaining the topological order of a directed acyclic graph (DAG) in the presence of edge insertions and deletions. We present a new algorithm and, although this has inferior time complexi...
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