1,329 research outputs found
Truss Decomposition in Massive Networks
The k-truss is a type of cohesive subgraphs proposed recently for the study
of networks. While the problem of computing most cohesive subgraphs is NP-hard,
there exists a polynomial time algorithm for computing k-truss. Compared with
k-core which is also efficient to compute, k-truss represents the "core" of a
k-core that keeps the key information of, while filtering out less important
information from, the k-core. However, existing algorithms for computing
k-truss are inefficient for handling today's massive networks. We first improve
the existing in-memory algorithm for computing k-truss in networks of moderate
size. Then, we propose two I/O-efficient algorithms to handle massive networks
that cannot fit in main memory. Our experiments on real datasets verify the
efficiency of our algorithms and the value of k-truss.Comment: VLDB201
Truly scalable K-Truss and max-truss algorithms for community detection in graphs
The notion of k-truss has been introduced a decade ago in social network analysis and security for community detection, as a form of cohesive subgraphs less stringent than a clique (set of pairwise linked nodes), and more selective than a k-core (induced subgraph with minimum degree k). A k-truss is an inclusion-maximal subgraph Hin which each edge belongs to at least k-2triangles inside H. The truss decomposition establishes, for each edge e, the maximum kfor which ebelongs to a k-truss. Analogously to the largest clique and to the maximum k-core, the strongest community for k-truss is the max-truss, which corresponds to the k-truss having the maximum k. Even though the computation of truss decomposition and of the max-truss takes polynomial time, on a large scale, it suffers from handling a potentially cubic number of wedges. In this paper, we provide a new algorithm FMT, which advances the state of the art on different sides: lower execution time, lower memory usage, and no need for expensive hardware. We compare FMT experimentally with the most recent state-of-the-art algorithms on a set of large real-world and synthetic networks with over a billion edges. The massive improvement allows FMT to compute the max-truss of networks of tens of billions of edges on a single standard server machine
Efficient Truss Maintenance in Evolving Networks
Truss was proposed to study social network data represented by graphs. A
k-truss of a graph is a cohesive subgraph, in which each edge is contained in
at least k-2 triangles within the subgraph. While truss has been demonstrated
as superior to model the close relationship in social networks and efficient
algorithms for finding trusses have been extensively studied, very little
attention has been paid to truss maintenance. However, most social networks are
evolving networks. It may be infeasible to recompute trusses from scratch from
time to time in order to find the up-to-date -trusses in the evolving
networks. In this paper, we discuss how to maintain trusses in a graph with
dynamic updates. We first discuss a set of properties on maintaining trusses,
then propose algorithms on maintaining trusses on edge deletions and
insertions, finally, we discuss truss index maintenance. We test the proposed
techniques on real datasets. The experiment results show the promise of our
work
Shared-memory Graph Truss Decomposition
We present PKT, a new shared-memory parallel algorithm and OpenMP
implementation for the truss decomposition of large sparse graphs. A k-truss is
a dense subgraph definition that can be considered a relaxation of a clique.
Truss decomposition refers to a partitioning of all the edges in the graph
based on their k-truss membership. The truss decomposition of a graph has many
applications. We show that our new approach PKT consistently outperforms other
truss decomposition approaches for a collection of large sparse graphs and on a
24-core shared-memory server. PKT is based on a recently proposed algorithm for
k-core decomposition.Comment: 10 pages, conference submissio
Approximate Closest Community Search in Networks
Recently, there has been significant interest in the study of the community
search problem in social and information networks: given one or more query
nodes, find densely connected communities containing the query nodes. However,
most existing studies do not address the "free rider" issue, that is, nodes far
away from query nodes and irrelevant to them are included in the detected
community. Some state-of-the-art models have attempted to address this issue,
but not only are their formulated problems NP-hard, they do not admit any
approximations without restrictive assumptions, which may not always hold in
practice.
In this paper, given an undirected graph G and a set of query nodes Q, we
study community search using the k-truss based community model. We formulate
our problem of finding a closest truss community (CTC), as finding a connected
k-truss subgraph with the largest k that contains Q, and has the minimum
diameter among such subgraphs. We prove this problem is NP-hard. Furthermore,
it is NP-hard to approximate the problem within a factor , for
any . However, we develop a greedy algorithmic framework,
which first finds a CTC containing Q, and then iteratively removes the furthest
nodes from Q, from the graph. The method achieves 2-approximation to the
optimal solution. To further improve the efficiency, we make use of a compact
truss index and develop efficient algorithms for k-truss identification and
maintenance as nodes get eliminated. In addition, using bulk deletion
optimization and local exploration strategies, we propose two more efficient
algorithms. One of them trades some approximation quality for efficiency while
the other is a very efficient heuristic. Extensive experiments on 6 real-world
networks show the effectiveness and efficiency of our community model and
search algorithms
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