13,592 research outputs found

    Revisiting Interval Graphs for Network Science

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    The vertices of an interval graph represent intervals over a real line where overlapping intervals denote that their corresponding vertices are adjacent. This implies that the vertices are measurable by a metric and there exists a linear structure in the system. The generalization is an embedding of a graph onto a multi-dimensional Euclidean space and it was used by scientists to study the multi-relational complexity of ecology. However the research went out of fashion in the 1980s and was not revisited when Network Science recently expressed interests with multi-relational networks known as multiplexes. This paper studies interval graphs from the perspective of Network Science

    Search in Power-Law Networks

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    Many communication and social networks have power-law link distributions, containing a few nodes which have a very high degree and many with low degree. The high connectivity nodes play the important role of hubs in communication and networking, a fact which can be exploited when designing efficient search algorithms. We introduce a number of local search strategies which utilize high degree nodes in power-law graphs and which have costs which scale sub-linearly with the size of the graph. We also demonstrate the utility of these strategies on the Gnutella peer-to-peer network.Comment: 17 pages, 14 figure

    Visual SLAM for flying vehicles

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    The ability to learn a map of the environment is important for numerous types of robotic vehicles. In this paper, we address the problem of learning a visual map of the ground using flying vehicles. We assume that the vehicles are equipped with one or two low-cost downlooking cameras in combination with an attitude sensor. Our approach is able to construct a visual map that can later on be used for navigation. Key advantages of our approach are that it is comparably easy to implement, can robustly deal with noisy camera images, and can operate either with a monocular camera or a stereo camera system. Our technique uses visual features and estimates the correspondences between features using a variant of the progressive sample consensus (PROSAC) algorithm. This allows our approach to extract spatial constraints between camera poses that can then be used to address the simultaneous localization and mapping (SLAM) problem by applying graph methods. Furthermore, we address the problem of efficiently identifying loop closures. We performed several experiments with flying vehicles that demonstrate that our method is able to construct maps of large outdoor and indoor environments. © 2008 IEEE

    The conduciveness of CA-rule graphs

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    Given two subsets A and B of nodes in a directed graph, the conduciveness of the graph from A to B is the ratio representing how many of the edges outgoing from nodes in A are incoming to nodes in B. When the graph's nodes stand for the possible solutions to certain problems of combinatorial optimization, choosing its edges appropriately has been shown to lead to conduciveness properties that provide useful insight into the performance of algorithms to solve those problems. Here we study the conduciveness of CA-rule graphs, that is, graphs whose node set is the set of all CA rules given a cell's number of possible states and neighborhood size. We consider several different edge sets interconnecting these nodes, both deterministic and random ones, and derive analytical expressions for the resulting graph's conduciveness toward rules having a fixed number of non-quiescent entries. We demonstrate that one of the random edge sets, characterized by allowing nodes to be sparsely interconnected across any Hamming distance between the corresponding rules, has the potential of providing reasonable conduciveness toward the desired rules. We conjecture that this may lie at the bottom of the best strategies known to date for discovering complex rules to solve specific problems, all of an evolutionary nature

    LASAGNE: Locality And Structure Aware Graph Node Embedding

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    In this work we propose Lasagne, a methodology to learn locality and structure aware graph node embeddings in an unsupervised way. In particular, we show that the performance of existing random-walk based approaches depends strongly on the structural properties of the graph, e.g., the size of the graph, whether the graph has a flat or upward-sloping Network Community Profile (NCP), whether the graph is expander-like, whether the classes of interest are more k-core-like or more peripheral, etc. For larger graphs with flat NCPs that are strongly expander-like, existing methods lead to random walks that expand rapidly, touching many dissimilar nodes, thereby leading to lower-quality vector representations that are less useful for downstream tasks. Rather than relying on global random walks or neighbors within fixed hop distances, Lasagne exploits strongly local Approximate Personalized PageRank stationary distributions to more precisely engineer local information into node embeddings. This leads, in particular, to more meaningful and more useful vector representations of nodes in poorly-structured graphs. We show that Lasagne leads to significant improvement in downstream multi-label classification for larger graphs with flat NCPs, that it is comparable for smaller graphs with upward-sloping NCPs, and that is comparable to existing methods for link prediction tasks
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