27,877 research outputs found
Cyclic schedules for r irregularly occurring event
Consider r irregular polygons with vertices on some circle. Authors explains how the polygons should be arranged to minimize some criterion function depending on the distances between adjacent vertices. A solution of this problem is given. It is based on a decomposition of the set of all schedules into local regions in which the optimization problem is convex. For the criterion functions minimize the maximum distance and maximize the minimum distance the local optimization problems are related to network flow problems which can be solved efficiently. If the sum of squared distances is to be minimized a locally optimal solution can be found by solving a system of linear equations. For fixed r the global problem is polynomially solvable for all the above-mentioned objective functions. In the general case, however, the global problem is NP-hard
Efficient computation of partition of unity interpolants through a block-based searching technique
In this paper we propose a new efficient interpolation tool, extremely
suitable for large scattered data sets. The partition of unity method is used
and performed by blending Radial Basis Functions (RBFs) as local approximants
and using locally supported weight functions. In particular we present a new
space-partitioning data structure based on a partition of the underlying
generic domain in blocks. This approach allows us to examine only a reduced
number of blocks in the search process of the nearest neighbour points, leading
to an optimized searching routine. Complexity analysis and numerical
experiments in two- and three-dimensional interpolation support our findings.
Some applications to geometric modelling are also considered. Moreover, the
associated software package written in \textsc{Matlab} is here discussed and
made available to the scientific community
Scalable Parallel Numerical Constraint Solver Using Global Load Balancing
We present a scalable parallel solver for numerical constraint satisfaction
problems (NCSPs). Our parallelization scheme consists of homogeneous worker
solvers, each of which runs on an available core and communicates with others
via the global load balancing (GLB) method. The parallel solver is implemented
with X10 that provides an implementation of GLB as a library. In experiments,
several NCSPs from the literature were solved and attained up to 516-fold
speedup using 600 cores of the TSUBAME2.5 supercomputer.Comment: To be presented at X10'15 Worksho
Polygon scheduling
Consider a set of circles of the same length and r irregular polygons with vertices on a circle of this length. Each of the polygons has to be arranged on a given subset of all circles and the positions of the polygon on the different circles are depending on each other. How should the polygons be arranged relative to each other to minimize some criterion function depending on the distances between adjacent vertices on all circles? A decomposition of the set of all arrangements of the polygons into local regions in which the optimization problem is convex is given. An exact description of the local regions and a sharp bound on the number of local regions are derived. For the criterion functions minimizing the maximum weighted distance, maximizing the minimum weighted distance, and minimizing the sum of weighted distances the local optimization problems can be reduced to polynomially solvable network flow problems
GLB: Lifeline-based Global Load Balancing library in X10
We present GLB, a programming model and an associated implementation that can
handle a wide range of irregular paral- lel programming problems running over
large-scale distributed systems. GLB is applicable both to problems that are
easily load-balanced via static scheduling and to problems that are hard to
statically load balance. GLB hides the intricate syn- chronizations (e.g.,
inter-node communication, initialization and startup, load balancing,
termination and result collection) from the users. GLB internally uses a
version of the lifeline graph based work-stealing algorithm proposed by
Saraswat et al. Users of GLB are simply required to write several pieces of
sequential code that comply with the GLB interface. GLB then schedules and
orchestrates the parallel execution of the code correctly and efficiently at
scale. We have applied GLB to two representative benchmarks: Betweenness
Centrality (BC) and Unbalanced Tree Search (UTS). Among them, BC can be
statically load-balanced whereas UTS cannot. In either case, GLB scales well--
achieving nearly linear speedup on different computer architectures (Power,
Blue Gene/Q, and K) -- up to 16K cores
Recent Advances in Graph Partitioning
We survey recent trends in practical algorithms for balanced graph
partitioning together with applications and future research directions
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