16,751 research outputs found
Porting Decision Tree Algorithms to Multicore using FastFlow
The whole computer hardware industry embraced multicores. For these machines,
the extreme optimisation of sequential algorithms is no longer sufficient to
squeeze the real machine power, which can be only exploited via thread-level
parallelism. Decision tree algorithms exhibit natural concurrency that makes
them suitable to be parallelised. This paper presents an approach for
easy-yet-efficient porting of an implementation of the C4.5 algorithm on
multicores. The parallel porting requires minimal changes to the original
sequential code, and it is able to exploit up to 7X speedup on an Intel
dual-quad core machine.Comment: 18 pages + cove
Incidence Geometries and the Pass Complexity of Semi-Streaming Set Cover
Set cover, over a universe of size , may be modelled as a data-streaming
problem, where the sets that comprise the instance are to be read one by
one. A semi-streaming algorithm is allowed only space to process this stream. For each , we give a very
simple deterministic algorithm that makes passes over the input stream and
returns an appropriately certified -approximation to the
optimum set cover. More importantly, we proceed to show that this approximation
factor is essentially tight, by showing that a factor better than
is unachievable for a -pass semi-streaming
algorithm, even allowing randomisation. In particular, this implies that
achieving a -approximation requires
passes, which is tight up to the factor. These results extend to a
relaxation of the set cover problem where we are allowed to leave an
fraction of the universe uncovered: the tight bounds on the best
approximation factor achievable in passes turn out to be
. Our lower bounds are based
on a construction of a family of high-rank incidence geometries, which may be
thought of as vast generalisations of affine planes. This construction, based
on algebraic techniques, appears flexible enough to find other applications and
is therefore interesting in its own right.Comment: 20 page
Parallel Algorithms for Geometric Graph Problems
We give algorithms for geometric graph problems in the modern parallel models
inspired by MapReduce. For example, for the Minimum Spanning Tree (MST) problem
over a set of points in the two-dimensional space, our algorithm computes a
-approximate MST. Our algorithms work in a constant number of
rounds of communication, while using total space and communication proportional
to the size of the data (linear space and near linear time algorithms). In
contrast, for general graphs, achieving the same result for MST (or even
connectivity) remains a challenging open problem, despite drawing significant
attention in recent years.
We develop a general algorithmic framework that, besides MST, also applies to
Earth-Mover Distance (EMD) and the transportation cost problem. Our algorithmic
framework has implications beyond the MapReduce model. For example it yields a
new algorithm for computing EMD cost in the plane in near-linear time,
. We note that while recently Sharathkumar and Agarwal
developed a near-linear time algorithm for -approximating EMD,
our algorithm is fundamentally different, and, for example, also solves the
transportation (cost) problem, raised as an open question in their work.
Furthermore, our algorithm immediately gives a -approximation
algorithm with space in the streaming-with-sorting model with
passes. As such, it is tempting to conjecture that the
parallel models may also constitute a concrete playground in the quest for
efficient algorithms for EMD (and other similar problems) in the vanilla
streaming model, a well-known open problem
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