Adjacency list

About: Adjacency list is a research topic. Over the lifetime, 4419 publications have been published within this topic receiving 78449 citations.

Degree-aware Hybrid Graph Traversal on FPGA-HMC Platform

Abstract: Graph traversal is a core primitive for graph analytics and a basis for many higher-level graph analysis methods. However, irregularities in the structure of scale-free graphs (e.g., social network) limit our ability to analyze these important and growing datasets. A key challenge is the redundant graph computations caused by the presence of high-degree vertices which not only increase the total amount of computations but also incur unnecessary random data access. In this paper, we present a graph processing system on an FPGA-HMC platform, based on software/hardware co-design and co- optimization. For the first time, we leverage the inherent graph property i.e. vertex degree to co-optimize algorithm and hardware architecture. In particular, we first develop two algorithm optimization techniques:degree-aware adjacency list reordering anddegree-aware vertex index sorting. The former can reduce the number of redundant graph computations, while the latter can create a strong correlation between vertex index and data access frequency, which can be effectively applied to guide the hardware design. We further implement the optimized hybrid graph traversal algorithm on an FPGA-HMC platform. By leveraging the strong correlation between vertex index and data access frequency made by degree-aware vertex index sorting, we develop two platform-dependent hardware optimization techniques, namely degree-aware data placement and degree-aware adjacency list compression. These two techniques together substantially reduce the amount of access to external memory. Finally, we conduct extensive experiments on an FPGA-HMC platform to verify the effectiveness of the proposed techniques. To the best of our knowledge, our implementation achieves the highest performance (45.8 billion traversed edges per second) among existing FPGA-based graph processing systems.

A nonparametric two-sample hypothesis testing problem for random dot product graphs

Abstract: nite-dimensional random dot product graphs have generating latent positions that are independently drawn from the same distribution, or distributions that are related via scaling or projection. We propose a test statistic that is a kernel-based function of the adjacency spectral embedding for each graph. We obtain a limiting distribution for our test statistic under the null and we show that our test procedure is consistent across a broad range of alternatives. 1. Introduction. The nonparametric two-sample hypothesis testing problem involves {Xi} n=1 i:i:d F; {Yk} m=1 i:i:d G; H0 F =G against HA F ~ =G where F and G are two distributions taking values in R d . This is a classical problem and there exist a large number of test statistics T({Xi} n=1 ;{Yk} m=1 ) that are consistent for any arbitrary distributions F and G. In this paper, we consider a related problem that arises naturally in the context of inference on random graphs. That is, suppose that the {Xi} n=1 and {Yk} m=1 are unobserved, and we observe instead adjacency matrices A and B corresponding to random dot product graphs on n and m vertices with latent positions {Xi} n=1 and {Yk} m=1 , respectively. Denoting by { ^ Xi} n=1 and { ^ Yk} m=1 the adjacency spectral embedding of A and B, we construct T({ ^ X} n=1 ;{ ^ Yk} m=1 ) for testing F =G (and related hypothesis) that is consistent for a broad collection of distributions. In other words, we construct a test for the hypothesis that two random dot product graphs have the same underlying distribution of latent positions, or underlying distributions that are related via scaling or projection. This formulation includes, as a special case, a test for whether two graphs come from the same stochastic blockmodel or from the same degree-corrected stochastic blockmodel. This problem may be viewed as the nonparametric analogue of the semiparametric inference problem considered in [30], in which a valid test is given for the hypothesis that two random dot product graphs have the same

Efficient Compression of Web Graphs

Abstract: Several methods have been proposed for compressing the linkage data of a Web graph. Among them, the method proposed by Boldi and Vigna is known as the most efficient one. In the paper, we propose a new method to compress a Web graph. Our method is more efficient than theirs with respect to the size of the compressed data. For example, our method needs only 1.99 bits per link to compress a Web graph containing 3,216,152 links connecting 325,557 pages, while the method of Boldi and Vigna needs 2.84 bits per link to compress the same Web graph.

Defining spatial entropy from multivariate distributions of co-occurrences

Abstract: Finding geographical patterns by analysing the spatial configuration distribution of events, objects or their attributes has a long history in geography, ecology and epidemiology. Measuring the presence of patterns, clusters, or comparing the spatial organisation for different attributes, symbols within the same map or for different maps, is often the basis of analysis. Landscape ecology has provided a long list of interesting indicators, e.g. summaries of patch size distribution. Looking at content information, the Shannon entropy is also a measure of a distribution providing insight into the organisation of data, and has been widely used for example in economical geography. Unfortunately, using the Shannon entropy on the bare distribution of categories within the spatial domain does not describe the spatial organisation itself. Particularly in ecology and geography, some authors have proposed integrating some spatial aspects into the entropy: using adjacency properties or distances between and within categories. This paper goes further with adjacency, emphasising the use of co-occurences of categories at multiple orders, the adjacency being seen as a particular co-occurence of order 2 with a distance of collocation null, and proposes a spatial entropy measure framework. The approach allows multivariate data with covariates to be accounted for, and provides the flexibility to design a wide range of spatial interaction models between the attributes. Generating a multivariate multinomial distribution of collocations describing the spatial organisation, allows the interaction to be assessed via an entropy formula. This spatial entropy is dependent on the distance of collocation used, which can be seen as a scale factor in the spatial organisation to be analysed.

Fuzzy geometry: An overview

Abstract: The author briefly reviews work on the fuzzy topology and geometry of image subsets, including adjacency, separation, and connectedness; distance and relative position; area, perimeter, and diameter; convexity and starshapedness; and medial axes and thinning. >