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Chippe : a system for constraint driven behavioral synthesis
This report describes the Chippe system, gives some background previous work and describes several sample design runs of the system. Also presented are the sources of the design tradeoffs used by Chippe, and overview of the internal design model, and experiences using the system
Massively Parallel Algorithms for Distance Approximation and Spanners
Over the past decade, there has been increasing interest in
distributed/parallel algorithms for processing large-scale graphs. By now, we
have quite fast algorithms -- usually sublogarithmic-time and often
-time, or even faster -- for a number of fundamental graph
problems in the massively parallel computation (MPC) model. This model is a
widely-adopted theoretical abstraction of MapReduce style settings, where a
number of machines communicate in an all-to-all manner to process large-scale
data. Contributing to this line of work on MPC graph algorithms, we present
round MPC algorithms for computing
-spanners in the strongly sublinear regime of local memory. To
the best of our knowledge, these are the first sublogarithmic-time MPC
algorithms for spanner construction. As primary applications of our spanners,
we get two important implications, as follows:
-For the MPC setting, we get an -round algorithm for
approximation of all pairs shortest paths (APSP) in the
near-linear regime of local memory. To the best of our knowledge, this is the
first sublogarithmic-time MPC algorithm for distance approximations.
-Our result above also extends to the Congested Clique model of distributed
computing, with the same round complexity and approximation guarantee. This
gives the first sub-logarithmic algorithm for approximating APSP in weighted
graphs in the Congested Clique model
Space and Time Efficient Parallel Graph Decomposition, Clustering, and Diameter Approximation
We develop a novel parallel decomposition strategy for unweighted, undirected
graphs, based on growing disjoint connected clusters from batches of centers
progressively selected from yet uncovered nodes. With respect to similar
previous decompositions, our strategy exercises a tighter control on both the
number of clusters and their maximum radius.
We present two important applications of our parallel graph decomposition:
(1) -center clustering approximation; and (2) diameter approximation. In
both cases, we obtain algorithms which feature a polylogarithmic approximation
factor and are amenable to a distributed implementation that is geared for
massive (long-diameter) graphs. The total space needed for the computation is
linear in the problem size, and the parallel depth is substantially sublinear
in the diameter for graphs with low doubling dimension. To the best of our
knowledge, ours are the first parallel approximations for these problems which
achieve sub-diameter parallel time, for a relevant class of graphs, using only
linear space. Besides the theoretical guarantees, our algorithms allow for a
very simple implementation on clustered architectures: we report on extensive
experiments which demonstrate their effectiveness and efficiency on large
graphs as compared to alternative known approaches.Comment: 14 page
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