9,435 research outputs found
An Approximate Maximum Common Subgraph Algorithm for Large Digital Circuits
This paper presents an approximate Maximum Common Subgraph (MCS) algorithm, specifically for directed, cyclic graphs representing digital circuits. \ud
Because of the application domain, the graphs have nice properties: they are very sparse; have many different labels; and most vertices have only one predecessor. The algorithm iterates over all vertices once and uses heuristics to find the MCS. It is linear in computational complexity with respect to the size of the graph. Experiments show that very large common subgraphs were found in graphs of up to 200,000 vertices within a few minutes, when a quarter or less of the graphs differ. The variation in run-time and quality of the result is low
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
A Partitioning Algorithm for Maximum Common Subgraph Problems
We introduce a new branch and bound algorithm for the maximum common subgraph and maximum common connected subgraph problems which is based around vertex labelling and partitioning. Our method in some ways resembles a traditional constraint programming approach, but uses a novel compact domain store and supporting inference algorithms which dramatically reduce the memory and computation requirements during search, and allow better dual viewpoint ordering heuristics to be calculated cheaply. Experiments show a speedup of more than an order of magnitude over the state of the art, and demonstrate that we can operate on much larger graphs without running out of memory
Eigenvector-based identification of bipartite subgraphs
We report our experiments in identifying large bipartite subgraphs of simple
connected graphs which are based on the sign pattern of eigenvectors belonging
to the extremal eigenvalues of different graph matrices: adjacency, signless
Laplacian, Laplacian, and normalized Laplacian matrix. We compare the
performance of these methods to a local switching algorithm based on the Erdos
bound that each graph contains a bipartite subgraph with at least half of its
edges. Experiments with one scale-free and three random graph models, which
cover a wide range of real-world networks, show that the methods based on the
eigenvectors of the normalized Laplacian and the adjacency matrix yield
slightly better, but comparable results to the local switching algorithm. We
also formulate two edge bipartivity indices based on the former eigenvectors,
and observe that the method of iterative removal of edges with maximum
bipartivity index until one obtains a bipartite subgraph, yields comparable
results to the local switching algorithm, and significantly better results than
an analogous method that employs the edge bipartivity index of Estrada and
Gomez-Gardenes.Comment: 20 pages, 8 figure
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