26,600 research outputs found
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
K-core decomposition of Internet graphs: hierarchies, self-similarity and measurement biases
We consider the -core decomposition of network models and Internet graphs
at the autonomous system (AS) level. The -core analysis allows to
characterize networks beyond the degree distribution and uncover structural
properties and hierarchies due to the specific architecture of the system. We
compare the -core structure obtained for AS graphs with those of several
network models and discuss the differences and similarities with the real
Internet architecture. The presence of biases and the incompleteness of the
real maps are discussed and their effect on the -core analysis is assessed
with numerical experiments simulating biased exploration on a wide range of
network models. We find that the -core analysis provides an interesting
characterization of the fluctuations and incompleteness of maps as well as
information helping to discriminate the original underlying structure
Distance-generalized Core Decomposition
The -core of a graph is defined as the maximal subgraph in which every
vertex is connected to at least other vertices within that subgraph. In
this work we introduce a distance-based generalization of the notion of
-core, which we refer to as the -core, i.e., the maximal subgraph in
which every vertex has at least other vertices at distance within
that subgraph. We study the properties of the -core showing that it
preserves many of the nice features of the classic core decomposition (e.g.,
its connection with the notion of distance-generalized chromatic number) and it
preserves its usefulness to speed-up or approximate distance-generalized
notions of dense structures, such as -club.
Computing the distance-generalized core decomposition over large networks is
intrinsically complex. However, by exploiting clever upper and lower bounds we
can partition the computation in a set of totally independent subcomputations,
opening the door to top-down exploration and to multithreading, and thus
achieving an efficient algorithm
On infinite-finite duality pairs of directed graphs
The (A,D) duality pairs play crucial role in the theory of general relational
structures and in the Constraint Satisfaction Problem. The case where both
classes are finite is fully characterized. The case when both side are infinite
seems to be very complex. It is also known that no finite-infinite duality pair
is possible if we make the additional restriction that both classes are
antichains. In this paper (which is the first one of a series) we start the
detailed study of the infinite-finite case.
Here we concentrate on directed graphs. We prove some elementary properties
of the infinite-finite duality pairs, including lower and upper bounds on the
size of D, and show that the elements of A must be equivalent to forests if A
is an antichain. Then we construct instructive examples, where the elements of
A are paths or trees. Note that the existence of infinite-finite antichain
dualities was not previously known
Performance metrics for consolidated servers
In spite of the widespread adoption of virtualization and consol- idation, there exists no consensus with respect to how to bench- mark consolidated servers that run multiple guest VMs on the same physical hardware. For example, VMware proposes VMmark which basically computes the geometric mean of normalized throughput values across the VMs; Intel uses vConsolidate which reports a weighted arithmetic average of normalized throughput values.
These benchmarking methodologies focus on total system through- put (i.e., across all VMs in the system), and do not take into account per-VM performance. We argue that a benchmarking methodology for consolidated servers should quantify both total system through- put and per-VM performance in order to provide a meaningful and precise performance characterization. We therefore present two performance metrics, Total Normalized Throughput (TNT) to characterize total system performance, and Average Normalized Reduced Throughput (ANRT) to characterize per-VM performance.
We compare TNT and ANRT against VMmark using published performance numbers, and report several cases for which the VM- mark score is misleading. This is, VMmark says one platform yields better performance than another, however, TNT and ANRT show that both platforms represent different trade-offs in total system throughput versus per-VM performance. Or, even worse, in a cou- ple cases we observe that VMmark yields opposite conclusions than TNT and ANRT, i.e., VMmark says one system performs better than another one which is contradicted by TNT/ANRT performance characterization
Core Decomposition in Multilayer Networks: Theory, Algorithms, and Applications
Multilayer networks are a powerful paradigm to model complex systems, where
multiple relations occur between the same entities. Despite the keen interest
in a variety of tasks, algorithms, and analyses in this type of network, the
problem of extracting dense subgraphs has remained largely unexplored so far.
In this work we study the problem of core decomposition of a multilayer
network. The multilayer context is much challenging as no total order exists
among multilayer cores; rather, they form a lattice whose size is exponential
in the number of layers. In this setting we devise three algorithms which
differ in the way they visit the core lattice and in their pruning techniques.
We then move a step forward and study the problem of extracting the
inner-most (also known as maximal) cores, i.e., the cores that are not
dominated by any other core in terms of their core index in all the layers.
Inner-most cores are typically orders of magnitude less than all the cores.
Motivated by this, we devise an algorithm that effectively exploits the
maximality property and extracts inner-most cores directly, without first
computing a complete decomposition.
Finally, we showcase the multilayer core-decomposition tool in a variety of
scenarios and problems. We start by considering the problem of densest-subgraph
extraction in multilayer networks. We introduce a definition of multilayer
densest subgraph that trades-off between high density and number of layers in
which the high density holds, and exploit multilayer core decomposition to
approximate this problem with quality guarantees. As further applications, we
show how to utilize multilayer core decomposition to speed-up the extraction of
frequent cross-graph quasi-cliques and to generalize the community-search
problem to the multilayer setting
k-core decomposition: a tool for the visualization of large scale networks
We use the k-core decomposition to visualize large scale complex networks in
two dimensions. This decomposition, based on a recursive pruning of the least
connected vertices, allows to disentangle the hierarchical structure of
networks by progressively focusing on their central cores. By using this
strategy we develop a general visualization algorithm that can be used to
compare the structural properties of various networks and highlight their
hierarchical structure. The low computational complexity of the algorithm,
O(n+e), where 'n' is the size of the network, and 'e' is the number of edges,
makes it suitable for the visualization of very large sparse networks. We apply
the proposed visualization tool to several real and synthetic graphs, showing
its utility in finding specific structural fingerprints of computer generated
and real world networks
Characterization and enumeration of toroidal K_{3,3}-subdivision-free graphs
We describe the structure of 2-connected non-planar toroidal graphs with no
K_{3,3}-subdivisions, using an appropriate substitution of planar networks into
the edges of certain graphs called toroidal cores. The structural result is
based on a refinement of the algorithmic results for graphs containing a fixed
K_5-subdivision in [A. Gagarin and W. Kocay, "Embedding graphs containing
K_5-subdivisions'', Ars Combin. 64 (2002), 33-49]. It allows to recognize these
graphs in linear-time and makes possible to enumerate labelled 2-connected
toroidal graphs containing no K_{3,3}-subdivisions and having minimum vertex
degree two or three by using an approach similar to [A. Gagarin, G. Labelle,
and P. Leroux, "Counting labelled projective-planar graphs without a
K_{3,3}-subdivision", submitted, arXiv:math.CO/0406140, (2004)].Comment: 18 pages, 7 figures and 4 table
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