6,635 research outputs found
Discriminative Distance-Based Network Indices with Application to Link Prediction
In large networks, using the length of shortest paths as the distance measure
has shortcomings. A well-studied shortcoming is that extending it to
disconnected graphs and directed graphs is controversial. The second
shortcoming is that a huge number of vertices may have exactly the same score.
The third shortcoming is that in many applications, the distance between two
vertices not only depends on the length of shortest paths, but also on the
number of shortest paths. In this paper, first we develop a new distance
measure between vertices of a graph that yields discriminative distance-based
centrality indices. This measure is proportional to the length of shortest
paths and inversely proportional to the number of shortest paths. We present
algorithms for exact computation of the proposed discriminative indices.
Second, we develop randomized algorithms that precisely estimate average
discriminative path length and average discriminative eccentricity and show
that they give -approximations of these indices. Third, we
perform extensive experiments over several real-world networks from different
domains. In our experiments, we first show that compared to the traditional
indices, discriminative indices have usually much more discriminability. Then,
we show that our randomized algorithms can very precisely estimate average
discriminative path length and average discriminative eccentricity, using only
few samples. Then, we show that real-world networks have usually a tiny average
discriminative path length, bounded by a constant (e.g., 2). Fourth, in order
to better motivate the usefulness of our proposed distance measure, we present
a novel link prediction method, that uses discriminative distance to decide
which vertices are more likely to form a link in future, and show its superior
performance compared to the well-known existing measures
Fast approximation of centrality and distances in hyperbolic graphs
We show that the eccentricities (and thus the centrality indices) of all
vertices of a -hyperbolic graph can be computed in linear
time with an additive one-sided error of at most , i.e., after a
linear time preprocessing, for every vertex of one can compute in
time an estimate of its eccentricity such that
for a small constant . We
prove that every -hyperbolic graph has a shortest path tree,
constructible in linear time, such that for every vertex of ,
. These results are based on an
interesting monotonicity property of the eccentricity function of hyperbolic
graphs: the closer a vertex is to the center of , the smaller its
eccentricity is. We also show that the distance matrix of with an additive
one-sided error of at most can be computed in
time, where is a small constant. Recent empirical studies show that
many real-world graphs (including Internet application networks, web networks,
collaboration networks, social networks, biological networks, and others) have
small hyperbolicity. So, we analyze the performance of our algorithms for
approximating centrality and distance matrix on a number of real-world
networks. Our experimental results show that the obtained estimates are even
better than the theoretical bounds.Comment: arXiv admin note: text overlap with arXiv:1506.01799 by other author
Performance Characterization of Multi-threaded Graph Processing Applications on Intel Many-Integrated-Core Architecture
Intel Xeon Phi many-integrated-core (MIC) architectures usher in a new era of
terascale integration. Among emerging killer applications, parallel graph
processing has been a critical technique to analyze connected data. In this
paper, we empirically evaluate various computing platforms including an Intel
Xeon E5 CPU, a Nvidia Geforce GTX1070 GPU and an Xeon Phi 7210 processor
codenamed Knights Landing (KNL) in the domain of parallel graph processing. We
show that the KNL gains encouraging performance when processing graphs, so that
it can become a promising solution to accelerating multi-threaded graph
applications. We further characterize the impact of KNL architectural
enhancements on the performance of a state-of-the art graph framework.We have
four key observations: 1 Different graph applications require distinctive
numbers of threads to reach the peak performance. For the same application,
various datasets need even different numbers of threads to achieve the best
performance. 2 Only a few graph applications benefit from the high bandwidth
MCDRAM, while others favor the low latency DDR4 DRAM. 3 Vector processing units
executing AVX512 SIMD instructions on KNLs are underutilized when running the
state-of-the-art graph framework. 4 The sub-NUMA cache clustering mode offering
the lowest local memory access latency hurts the performance of graph
benchmarks that are lack of NUMA awareness. At last, We suggest future works
including system auto-tuning tools and graph framework optimizations to fully
exploit the potential of KNL for parallel graph processing.Comment: published as L. Jiang, L. Chen and J. Qiu, "Performance
Characterization of Multi-threaded Graph Processing Applications on
Many-Integrated-Core Architecture," 2018 IEEE International Symposium on
Performance Analysis of Systems and Software (ISPASS), Belfast, United
Kingdom, 2018, pp. 199-20
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