35,571 research outputs found
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
Fast Computation of Small Cuts via Cycle Space Sampling
We describe a new sampling-based method to determine cuts in an undirected
graph. For a graph (V, E), its cycle space is the family of all subsets of E
that have even degree at each vertex. We prove that with high probability,
sampling the cycle space identifies the cuts of a graph. This leads to simple
new linear-time sequential algorithms for finding all cut edges and cut pairs
(a set of 2 edges that form a cut) of a graph.
In the model of distributed computing in a graph G=(V, E) with O(log V)-bit
messages, our approach yields faster algorithms for several problems. The
diameter of G is denoted by Diam, and the maximum degree by Delta. We obtain
simple O(Diam)-time distributed algorithms to find all cut edges,
2-edge-connected components, and cut pairs, matching or improving upon previous
time bounds. Under natural conditions these new algorithms are universally
optimal --- i.e. a Omega(Diam)-time lower bound holds on every graph. We obtain
a O(Diam+Delta/log V)-time distributed algorithm for finding cut vertices; this
is faster than the best previous algorithm when Delta, Diam = O(sqrt(V)). A
simple extension of our work yields the first distributed algorithm with
sub-linear time for 3-edge-connected components. The basic distributed
algorithms are Monte Carlo, but they can be made Las Vegas without increasing
the asymptotic complexity.
In the model of parallel computing on the EREW PRAM our approach yields a
simple algorithm with optimal time complexity O(log V) for finding cut pairs
and 3-edge-connected components.Comment: Previous version appeared in Proc. 35th ICALP, pages 145--160, 200
Linear Time Subgraph Counting, Graph Degeneracy, and the Chasm at Size Six
We consider the problem of counting all k-vertex subgraphs in an input graph, for any constant k. This problem (denoted SUB-CNT_k) has been studied extensively in both theory and practice. In a classic result, Chiba and Nishizeki (SICOMP 85) gave linear time algorithms for clique and 4-cycle counting for bounded degeneracy graphs. This is a rich class of sparse graphs that contains, for example, all minor-free families and preferential attachment graphs. The techniques from this result have inspired a number of recent practical algorithms for SUB-CNT_k. Towards a better understanding of the limits of these techniques, we ask: for what values of k can SUB_CNT_k be solved in linear time?
We discover a chasm at k=6. Specifically, we prove that for k < 6, SUB_CNT_k can be solved in linear time. Assuming a standard conjecture in fine-grained complexity, we prove that for all k ? 6, SUB-CNT_k cannot be solved even in near-linear time
Tensor Spectral Clustering for Partitioning Higher-order Network Structures
Spectral graph theory-based methods represent an important class of tools for
studying the structure of networks. Spectral methods are based on a first-order
Markov chain derived from a random walk on the graph and thus they cannot take
advantage of important higher-order network substructures such as triangles,
cycles, and feed-forward loops. Here we propose a Tensor Spectral Clustering
(TSC) algorithm that allows for modeling higher-order network structures in a
graph partitioning framework. Our TSC algorithm allows the user to specify
which higher-order network structures (cycles, feed-forward loops, etc.) should
be preserved by the network clustering. Higher-order network structures of
interest are represented using a tensor, which we then partition by developing
a multilinear spectral method. Our framework can be applied to discovering
layered flows in networks as well as graph anomaly detection, which we
illustrate on synthetic networks. In directed networks, a higher-order
structure of particular interest is the directed 3-cycle, which captures
feedback loops in networks. We demonstrate that our TSC algorithm produces
large partitions that cut fewer directed 3-cycles than standard spectral
clustering algorithms.Comment: SDM 201
Holistic Influence Maximization: Combining Scalability and Efficiency with Opinion-Aware Models
The steady growth of graph data from social networks has resulted in
wide-spread research in finding solutions to the influence maximization
problem. In this paper, we propose a holistic solution to the influence
maximization (IM) problem. (1) We introduce an opinion-cum-interaction (OI)
model that closely mirrors the real-world scenarios. Under the OI model, we
introduce a novel problem of Maximizing the Effective Opinion (MEO) of
influenced users. We prove that the MEO problem is NP-hard and cannot be
approximated within a constant ratio unless P=NP. (2) We propose a heuristic
algorithm OSIM to efficiently solve the MEO problem. To better explain the OSIM
heuristic, we first introduce EaSyIM - the opinion-oblivious version of OSIM, a
scalable algorithm capable of running within practical compute times on
commodity hardware. In addition to serving as a fundamental building block for
OSIM, EaSyIM is capable of addressing the scalability aspect - memory
consumption and running time, of the IM problem as well.
Empirically, our algorithms are capable of maintaining the deviation in the
spread always within 5% of the best known methods in the literature. In
addition, our experiments show that both OSIM and EaSyIM are effective,
efficient, scalable and significantly enhance the ability to analyze real
datasets.Comment: ACM SIGMOD Conference 2016, 18 pages, 29 figure
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