2,145 research outputs found
Enumerating Subgraph Instances Using Map-Reduce
The theme of this paper is how to find all instances of a given "sample"
graph in a larger "data graph," using a single round of map-reduce. For the
simplest sample graph, the triangle, we improve upon the best known such
algorithm. We then examine the general case, considering both the communication
cost between mappers and reducers and the total computation cost at the
reducers. To minimize communication cost, we exploit the techniques of (Afrati
and Ullman, TKDE 2011)for computing multiway joins (evaluating conjunctive
queries) in a single map-reduce round. Several methods are shown for
translating sample graphs into a union of conjunctive queries with as few
queries as possible. We also address the matter of optimizing computation cost.
Many serial algorithms are shown to be "convertible," in the sense that it is
possible to partition the data graph, explore each partition in a separate
reducer, and have the total computation cost at the reducers be of the same
order as the computation cost of the serial algorithm.Comment: 37 page
The Hardness of Embedding Grids and Walls
The dichotomy conjecture for the parameterized embedding problem states that
the problem of deciding whether a given graph from some class of
"pattern graphs" can be embedded into a given graph (that is, is isomorphic
to a subgraph of ) is fixed-parameter tractable if is a class of graphs
of bounded tree width and -complete otherwise.
Towards this conjecture, we prove that the embedding problem is
-complete if is the class of all grids or the class of all walls
Experimental Investigation of a 16-inch Impulse-type Supersonic-compressor Rotor
Performance data and characteristics of a 16-inch impulse-type supersonic-compressor rotor are presented. The experimental portion of this investigation was conducted in Freon-12. A peak pressure ratio of 3.6 was obtained with an adiabatic efficiency of 0.80 at design conditions. Performance was continuous from impulse operation, at open throttle, to shock-in-rotor operation at the stall condition
Acceptability with general orderings
We present a new approach to termination analysis of logic programs. The
essence of the approach is that we make use of general orderings (instead of
level mappings), like it is done in transformational approaches to logic
program termination analysis, but we apply these orderings directly to the
logic program and not to the term-rewrite system obtained through some
transformation. We define some variants of acceptability, based on general
orderings, and show how they are equivalent to LD-termination. We develop a
demand driven, constraint-based approach to verify these
acceptability-variants.
The advantage of the approach over standard acceptability is that in some
cases, where complex level mappings are needed, fairly simple orderings may be
easily generated. The advantage over transformational approaches is that it
avoids the transformation step all together.
{\bf Keywords:} termination analysis, acceptability, orderings.Comment: To appear in "Computational Logic: From Logic Programming into the
Future
GYM: A Multiround Distributed Join Algorithm
Multiround algorithms are now commonly used in distributed data processing systems, yet the extent to which algorithms can benefit from running more rounds is not well understood. This paper answers this question for several rounds for the problem of computing the equijoin of n relations. Given any query Q with width w, intersection width iw, input size IN, output size OUT, and a cluster of machines with M=Omega(IN frac{1}{epsilon}) memory available per machine, where epsilon > 1 and w ge 1 are constants, we show that:
1. Q can be computed in O(n) rounds with O(n(INw + OUT)2/M) communication cost with high probability.
Q can be computed in O(log(n)) rounds with O(n(INmax(w, 3iw) + OUT)2/M) communication cost with high probability.
Intersection width is a new notion we introduce for queries and generalized hypertree decompositions (GHDs) of queries that captures how connected the adjacent components of the GHDs are.
We achieve our first result by introducing a distributed and generalized version of Yannakakis\u27s algorithm, called GYM. GYM takes as input any GHD of Q with width w and depth d, and computes Q in O(d + log(n)) rounds and O(n (INw + OUT)2/M) communication cost. We achieve our second result by showing how to construct GHDs of Q with width max(w, 3iw) and depth O(log(n)). We describe another technique to construct GHDs with longer widths and lower depths, demonstrating other tradeoffs one can make between communication and the number of rounds
Assessing the impact of Laurentide Ice Sheet topography on glacial climate
Simulations of past climates require altered boundary conditions to account
for known shifts in the Earth system. For the Last Glacial Maximum (LGM) and
subsequent deglaciation, the existence of large Northern Hemisphere ice
sheets caused profound changes in surface topography and albedo. While
ice-sheet extent is fairly well known, numerous conflicting reconstructions
of ice-sheet topography suggest that precision in this boundary condition is
lacking. Here we use a high-resolution and oxygen-isotope-enabled
fully coupled global circulation model (GCM) (GISS ModelE2-R), along with
two different reconstructions of the Laurentide Ice Sheet (LIS) that provide
maximum and minimum estimates of LIS elevation, to assess the range of
climate variability in response to uncertainty in this boundary condition.
We present this comparison at two equilibrium time slices: the LGM, when
differences in ice-sheet topography are maximized, and 14 ka, when
differences in maximum ice-sheet height are smaller but still exist.
Overall, we find significant differences in the climate response to LIS
topography, with the larger LIS resulting in enhanced Atlantic Meridional
Overturning Circulation and warmer surface air temperatures, particularly
over northeastern Asia and the North Pacific. These up- and downstream effects
are associated with differences in the development of planetary waves in the
upper atmosphere, with the larger LIS resulting in a weaker trough over
northeastern Asia that leads to the warmer temperatures and decreased albedo
from snow and sea-ice cover. Differences between the 14 ka simulations are
similar in spatial extent but smaller in magnitude, suggesting that climate
is responding primarily to the larger difference in maximum LIS elevation in
the LGM simulations. These results suggest that such uncertainty in
ice-sheet boundary conditions alone may significantly impact the results of
paleoclimate simulations and their ability to successfully simulate past
climates, with implications for estimating climate sensitivity to greenhouse
gas forcing utilizing past climate states
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