136,342 research outputs found
A Multiscale Pyramid Transform for Graph Signals
Multiscale transforms designed to process analog and discrete-time signals
and images cannot be directly applied to analyze high-dimensional data residing
on the vertices of a weighted graph, as they do not capture the intrinsic
geometric structure of the underlying graph data domain. In this paper, we
adapt the Laplacian pyramid transform for signals on Euclidean domains so that
it can be used to analyze high-dimensional data residing on the vertices of a
weighted graph. Our approach is to study existing methods and develop new
methods for the four fundamental operations of graph downsampling, graph
reduction, and filtering and interpolation of signals on graphs. Equipped with
appropriate notions of these operations, we leverage the basic multiscale
constructs and intuitions from classical signal processing to generate a
transform that yields both a multiresolution of graphs and an associated
multiresolution of a graph signal on the underlying sequence of graphs.Comment: 16 pages, 13 figure
Subgraph Pattern Matching over Uncertain Graphs with Identity Linkage Uncertainty
There is a growing need for methods which can capture uncertainties and
answer queries over graph-structured data. Two common types of uncertainty are
uncertainty over the attribute values of nodes and uncertainty over the
existence of edges. In this paper, we combine those with identity uncertainty.
Identity uncertainty represents uncertainty over the mapping from objects
mentioned in the data, or references, to the underlying real-world entities. We
propose the notion of a probabilistic entity graph (PEG), a probabilistic graph
model that defines a distribution over possible graphs at the entity level. The
model takes into account node attribute uncertainty, edge existence
uncertainty, and identity uncertainty, and thus enables us to systematically
reason about all three types of uncertainties in a uniform manner. We introduce
a general framework for constructing a PEG given uncertain data at the
reference level and develop highly efficient algorithms to answer subgraph
pattern matching queries in this setting. Our algorithms are based on two novel
ideas: context-aware path indexing and reduction by join-candidates, which
drastically reduce the query search space. A comprehensive experimental
evaluation shows that our approach outperforms baseline implementations by
orders of magnitude
Scalable Breadth-First Search on a GPU Cluster
On a GPU cluster, the ratio of high computing power to communication
bandwidth makes scaling breadth-first search (BFS) on a scale-free graph
extremely challenging. By separating high and low out-degree vertices, we
present an implementation with scalable computation and a model for scalable
communication for BFS and direction-optimized BFS. Our communication model uses
global reduction for high-degree vertices, and point-to-point transmission for
low-degree vertices. Leveraging the characteristics of degree separation, we
reduce the graph size to one third of the conventional edge list
representation. With several other optimizations, we observe linear weak
scaling as we increase the number of GPUs, and achieve 259.8 GTEPS on a
scale-33 Graph500 RMAT graph with 124 GPUs on the latest CORAL early access
system.Comment: 12 pages, 13 figures. To appear at IPDPS 201
Gunrock: GPU Graph Analytics
For large-scale graph analytics on the GPU, the irregularity of data access
and control flow, and the complexity of programming GPUs, have presented two
significant challenges to developing a programmable high-performance graph
library. "Gunrock", our graph-processing system designed specifically for the
GPU, uses a high-level, bulk-synchronous, data-centric abstraction focused on
operations on a vertex or edge frontier. Gunrock achieves a balance between
performance and expressiveness by coupling high performance GPU computing
primitives and optimization strategies with a high-level programming model that
allows programmers to quickly develop new graph primitives with small code size
and minimal GPU programming knowledge. We characterize the performance of
various optimization strategies and evaluate Gunrock's overall performance on
different GPU architectures on a wide range of graph primitives that span from
traversal-based algorithms and ranking algorithms, to triangle counting and
bipartite-graph-based algorithms. The results show that on a single GPU,
Gunrock has on average at least an order of magnitude speedup over Boost and
PowerGraph, comparable performance to the fastest GPU hardwired primitives and
CPU shared-memory graph libraries such as Ligra and Galois, and better
performance than any other GPU high-level graph library.Comment: 52 pages, invited paper to ACM Transactions on Parallel Computing
(TOPC), an extended version of PPoPP'16 paper "Gunrock: A High-Performance
Graph Processing Library on the GPU
Window-based Streaming Graph Partitioning Algorithm
In the recent years, the scale of graph datasets has increased to such a
degree that a single machine is not capable of efficiently processing large
graphs. Thereby, efficient graph partitioning is necessary for those large
graph applications. Traditional graph partitioning generally loads the whole
graph data into the memory before performing partitioning; this is not only a
time consuming task but it also creates memory bottlenecks. These issues of
memory limitation and enormous time complexity can be resolved using
stream-based graph partitioning. A streaming graph partitioning algorithm reads
vertices once and assigns that vertex to a partition accordingly. This is also
called an one-pass algorithm. This paper proposes an efficient window-based
streaming graph partitioning algorithm called WStream. The WStream algorithm is
an edge-cut partitioning algorithm, which distributes a vertex among the
partitions. Our results suggest that the WStream algorithm is able to partition
large graph data efficiently while keeping the load balanced across different
partitions, and communication to a minimum. Evaluation results with real
workloads also prove the effectiveness of our proposed algorithm, and it
achieves a significant reduction in load imbalance and edge-cut with different
ranges of dataset
- …