9,093 research outputs found
Cut Tree Construction from Massive Graphs
The construction of cut trees (also known as Gomory-Hu trees) for a given
graph enables the minimum-cut size of the original graph to be obtained for any
pair of vertices. Cut trees are a powerful back-end for graph management and
mining, as they support various procedures related to the minimum cut, maximum
flow, and connectivity. However, the crucial drawback with cut trees is the
computational cost of their construction. In theory, a cut tree is built by
applying a maximum flow algorithm for times, where is the number of
vertices. Therefore, naive implementations of this approach result in cubic
time complexity, which is obviously too slow for today's large-scale graphs. To
address this issue, in the present study, we propose a new cut-tree
construction algorithm tailored to real-world networks. Using a series of
experiments, we demonstrate that the proposed algorithm is several orders of
magnitude faster than previous algorithms and it can construct cut trees for
billion-scale graphs.Comment: Short version will appear at ICDM'1
JGraphT -- A Java library for graph data structures and algorithms
Mathematical software and graph-theoretical algorithmic packages to
efficiently model, analyze and query graphs are crucial in an era where
large-scale spatial, societal and economic network data are abundantly
available. One such package is JGraphT, a programming library which contains
very efficient and generic graph data-structures along with a large collection
of state-of-the-art algorithms. The library is written in Java with stability,
interoperability and performance in mind. A distinctive feature of this library
is the ability to model vertices and edges as arbitrary objects, thereby
permitting natural representations of many common networks including
transportation, social and biological networks. Besides classic graph
algorithms such as shortest-paths and spanning-tree algorithms, the library
contains numerous advanced algorithms: graph and subgraph isomorphism; matching
and flow problems; approximation algorithms for NP-hard problems such as
independent set and TSP; and several more exotic algorithms such as Berge graph
detection. Due to its versatility and generic design, JGraphT is currently used
in large-scale commercial, non-commercial and academic research projects. In
this work we describe in detail the design and underlying structure of the
library, and discuss its most important features and algorithms. A
computational study is conducted to evaluate the performance of JGraphT versus
a number of similar libraries. Experiments on a large number of graphs over a
variety of popular algorithms show that JGraphT is highly competitive with
other established libraries such as NetworkX or the BGL.Comment: Major Revisio
Scalable Online Betweenness Centrality in Evolving Graphs
Betweenness centrality is a classic measure that quantifies the importance of
a graph element (vertex or edge) according to the fraction of shortest paths
passing through it. This measure is notoriously expensive to compute, and the
best known algorithm runs in O(nm) time. The problems of efficiency and
scalability are exacerbated in a dynamic setting, where the input is an
evolving graph seen edge by edge, and the goal is to keep the betweenness
centrality up to date. In this paper we propose the first truly scalable
algorithm for online computation of betweenness centrality of both vertices and
edges in an evolving graph where new edges are added and existing edges are
removed. Our algorithm is carefully engineered with out-of-core techniques and
tailored for modern parallel stream processing engines that run on clusters of
shared-nothing commodity hardware. Hence, it is amenable to real-world
deployment. We experiment on graphs that are two orders of magnitude larger
than previous studies. Our method is able to keep the betweenness centrality
measures up to date online, i.e., the time to update the measures is smaller
than the inter-arrival time between two consecutive updates.Comment: 15 pages, 9 Figures, accepted for publication in IEEE Transactions on
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