23,418 research outputs found
GoFFish: A Sub-Graph Centric Framework for Large-Scale Graph Analytics
Large scale graph processing is a major research area for Big Data
exploration. Vertex centric programming models like Pregel are gaining traction
due to their simple abstraction that allows for scalable execution on
distributed systems naturally. However, there are limitations to this approach
which cause vertex centric algorithms to under-perform due to poor compute to
communication overhead ratio and slow convergence of iterative superstep. In
this paper we introduce GoFFish a scalable sub-graph centric framework
co-designed with a distributed persistent graph storage for large scale graph
analytics on commodity clusters. We introduce a sub-graph centric programming
abstraction that combines the scalability of a vertex centric approach with the
flexibility of shared memory sub-graph computation. We map Connected
Components, SSSP and PageRank algorithms to this model to illustrate its
flexibility. Further, we empirically analyze GoFFish using several real world
graphs and demonstrate its significant performance improvement, orders of
magnitude in some cases, compared to Apache Giraph, the leading open source
vertex centric implementation.Comment: Under review by a conference, 201
Parallel distributed algorithms of the beta-model of the small world graphs
The research goal is to develop a large-scale agent-based simulation environment to support implementations of Internet simulation applications.The Small Worlds (SW) graphs are used to model Web sites and social networks of Internet users. Each vertex represents the identity of a simple agent. In order to cope with scalability issues, we have to consider distributed parallel
processing. The focus of this paper is to present two parallel-distributed algorithms for the construction of a particular type of SW graph called Beta-model. The first algorithm serializes the graph construction, while the second constructs the graph in parallel
A tree-decomposed transfer matrix for computing exact Potts model partition functions for arbitrary graphs, with applications to planar graph colourings
Combining tree decomposition and transfer matrix techniques provides a very
general algorithm for computing exact partition functions of statistical models
defined on arbitrary graphs. The algorithm is particularly efficient in the
case of planar graphs. We illustrate it by computing the Potts model partition
functions and chromatic polynomials (the number of proper vertex colourings
using Q colours) for large samples of random planar graphs with up to N=100
vertices. In the latter case, our algorithm yields a sub-exponential average
running time of ~ exp(1.516 sqrt(N)), a substantial improvement over the
exponential running time ~ exp(0.245 N) provided by the hitherto best known
algorithm. We study the statistics of chromatic roots of random planar graphs
in some detail, comparing the findings with results for finite pieces of a
regular lattice.Comment: 5 pages, 3 figures. Version 2 has been substantially expanded.
Version 3 shows that the worst-case running time is sub-exponential in the
number of vertice
Dichotomy for tree-structured trigraph list homomorphism problems
Trigraph list homomorphism problems (also known as list matrix partition
problems) have generated recent interest, partly because there are concrete
problems that are not known to be polynomial time solvable or NP-complete. Thus
while digraph list homomorphism problems enjoy dichotomy (each problem is
NP-complete or polynomial time solvable), such dichotomy is not necessarily
expected for trigraph list homomorphism problems. However, in this paper, we
identify a large class of trigraphs for which list homomorphism problems do
exhibit a dichotomy. They consist of trigraphs with a tree-like structure, and,
in particular, include all trigraphs whose underlying graphs are trees. In
fact, we show that for these tree-like trigraphs, the trigraph list
homomorphism problem is polynomially equivalent to a related digraph list
homomorphism problem. We also describe a few examples illustrating that our
conditions defining tree-like trigraphs are not unnatural, as relaxing them may
lead to harder problems
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