238,093 research outputs found
Efficient Subgraph Matching on Billion Node Graphs
The ability to handle large scale graph data is crucial to an increasing
number of applications. Much work has been dedicated to supporting basic graph
operations such as subgraph matching, reachability, regular expression
matching, etc. In many cases, graph indices are employed to speed up query
processing. Typically, most indices require either super-linear indexing time
or super-linear indexing space. Unfortunately, for very large graphs,
super-linear approaches are almost always infeasible. In this paper, we study
the problem of subgraph matching on billion-node graphs. We present a novel
algorithm that supports efficient subgraph matching for graphs deployed on a
distributed memory store. Instead of relying on super-linear indices, we use
efficient graph exploration and massive parallel computing for query
processing. Our experimental results demonstrate the feasibility of performing
subgraph matching on web-scale graph data.Comment: VLDB201
GraphMatch: Efficient Large-Scale Graph Construction for Structure from Motion
We present GraphMatch, an approximate yet efficient method for building the
matching graph for large-scale structure-from-motion (SfM) pipelines. Unlike
modern SfM pipelines that use vocabulary (Voc.) trees to quickly build the
matching graph and avoid a costly brute-force search of matching image pairs,
GraphMatch does not require an expensive offline pre-processing phase to
construct a Voc. tree. Instead, GraphMatch leverages two priors that can
predict which image pairs are likely to match, thereby making the matching
process for SfM much more efficient. The first is a score computed from the
distance between the Fisher vectors of any two images. The second prior is
based on the graph distance between vertices in the underlying matching graph.
GraphMatch combines these two priors into an iterative "sample-and-propagate"
scheme similar to the PatchMatch algorithm. Its sampling stage uses Fisher
similarity priors to guide the search for matching image pairs, while its
propagation stage explores neighbors of matched pairs to find new ones with a
high image similarity score. Our experiments show that GraphMatch finds the
most image pairs as compared to competing, approximate methods while at the
same time being the most efficient.Comment: Published at IEEE 3DV 201
Seeded Graph Matching: Efficient Algorithms and Theoretical Guarantees
In this paper, a new information theoretic framework for graph matching is
introduced. Using this framework, the graph isomorphism and seeded graph
matching problems are studied. The maximum degree algorithm for graph
isomorphism is analyzed and sufficient conditions for successful matching are
rederived using type analysis. Furthermore, a new seeded matching algorithm
with polynomial time complexity is introduced. The algorithm uses `typicality
matching' and techniques from point-to-point communications for reliable
matching. Assuming an Erdos-Renyi model on the correlated graph pair, it is
shown that successful matching is guaranteed when the number of seeds grows
logarithmically with the number of vertices in the graphs. The logarithmic
coefficient is shown to be inversely proportional to the mutual information
between the edge variables in the two graphs
Many-to-Many Graph Matching: a Continuous Relaxation Approach
Graphs provide an efficient tool for object representation in various
computer vision applications. Once graph-based representations are constructed,
an important question is how to compare graphs. This problem is often
formulated as a graph matching problem where one seeks a mapping between
vertices of two graphs which optimally aligns their structure. In the classical
formulation of graph matching, only one-to-one correspondences between vertices
are considered. However, in many applications, graphs cannot be matched
perfectly and it is more interesting to consider many-to-many correspondences
where clusters of vertices in one graph are matched to clusters of vertices in
the other graph. In this paper, we formulate the many-to-many graph matching
problem as a discrete optimization problem and propose an approximate algorithm
based on a continuous relaxation of the combinatorial problem. We compare our
method with other existing methods on several benchmark computer vision
datasets.Comment: 1
Structural graph matching using the EM algorithm and singular value decomposition
This paper describes an efficient algorithm for inexact graph matching. The method is purely structural, that is, it uses only the edge or connectivity structure of the graph and does not draw on node or edge attributes. We make two contributions: 1) commencing from a probability distribution for matching errors, we show how the problem of graph matching can be posed as maximum-likelihood estimation using the apparatus of the EM algorithm; and 2) we cast the recovery of correspondence matches between the graph nodes in a matrix framework. This allows one to efficiently recover correspondence matches using the singular value decomposition. We experiment with the method on both real-world and synthetic data. Here, we demonstrate that the method offers comparable performance to more computationally demanding method
Bigraphs with sharing
Bigraphical Reactive Systems (BRS) were designed by Milner as a universal formalism for modelling systems that evolve in time, locality, co-locality and connectivity. But the underlying model of location (the place graph) is a forest, which means there is no straightforward representation of locations that can overlap or intersect. This occurs in many domains, for example in wireless signalling, social interactions and audio communications. Here, we define bigraphs with sharing, which solves this problem by an extension of the basic formalism: we define the place graph as a directed acyclic graph, thus allowing a natural representation of overlapping or intersecting locations. We give a complete presentation of the theory of bigraphs with sharing, including a categorical semantics, algebraic properties, and several essential procedures for computation: bigraph with sharing matching, a SAT encoding of matching, and checking a fragment of the logic BiLog. We show that matching is an instance of the NP-complete sub-graph isomorphism problem and our approach based on a SAT encoding is also efficient for standard bigraphs. We give an overview of BigraphER (Bigraph Evaluator & Rewriting), an efficient implementation of bigraphs with sharing that provides manipulation, simulation and visualisation. The matching engine is based on the SAT encoding of the matching algorithm. Examples from the 802.11 CSMA/CA RTS/CTS protocol and a network management support system illustrate the applicability of the new theory
- …