836 research outputs found
Quasiconvex Programming
We define quasiconvex programming, a form of generalized linear programming
in which one seeks the point minimizing the pointwise maximum of a collection
of quasiconvex functions. We survey algorithms for solving quasiconvex programs
either numerically or via generalizations of the dual simplex method from
linear programming, and describe varied applications of this geometric
optimization technique in meshing, scientific computation, information
visualization, automated algorithm analysis, and robust statistics.Comment: 33 pages, 14 figure
Design and Analysis of Optical Interconnection Networks for Parallel Computation.
In this doctoral research, we propose several novel protocols and topologies for the interconnection of massively parallel processors. These new technologies achieve considerable improvements in system performance and structure simplicity. Currently, synchronous protocols are used in optical TDM buses. The major disadvantage of a synchronous protocol is the waste of packet slots. To offset this inherent drawback of synchronous TDM, a pipelined asynchronous TDM optical bus is proposed. The simulation results show that the performance of the proposed bus is significantly better than that of known pipelined synchronous TDM optical buses. Practically, the computation power of the plain TDM protocol is limited. Various extensions must be added to the system. In this research, a new pipelined optical TDM bus for implementing a linear array parallel computer architecture is proposed. The switches on the receiving segment of the bus can be dynamically controlled, which make the system highly reconfigurable. To build large and scalable systems, we need new network architectures that are suitable for optical interconnections. A new kind of reconfigurable bus called segmented bus is introduced to achieve reduced structure simplicity and increased concurrency. We show that parallel architectures based on segmented buses are versatile by showing that it can simulate parallel communication patterns supported by a wide variety of networks with small slowdown factors. New kinds of interconnection networks, the hypernetworks, have been proposed recently. Compared with point-to-point networks, they allow for increased resource-sharing and communication bandwidth utilization, and they are especially suitable for optical interconnects. One way to derive a hypernetwork is by finding the dual of a point-to-point network. Hypercube Q\sb{n}, where n is the dimension, is a very popular point-to-point network. It is interesting to construct hypernetworks from the dual Q\sbsp{n}{*} of hypercube of Q\sb{n}. In this research, the properties of Q\sbsp{n}{*} are investigated and a set of fundamental data communication algorithms for Q\sbsp{n}{*} are presented. The results indicate that the Q\sbsp{n}{*} hypernetwork is a useful and promising interconnection structure for high-performance parallel and distributed computing systems
Complementary vertices and adjacency testing in polytopes
Our main theoretical result is that, if a simple polytope has a pair of
complementary vertices (i.e., two vertices with no facets in common), then it
has at least two such pairs, which can be chosen to be disjoint. Using this
result, we improve adjacency testing for vertices in both simple and non-simple
polytopes: given a polytope in the standard form {x \in R^n | Ax = b and x \geq
0} and a list of its V vertices, we describe an O(n) test to identify whether
any two given vertices are adjacent. For simple polytopes this test is perfect;
for non-simple polytopes it may be indeterminate, and instead acts as a filter
to identify non-adjacent pairs. Our test requires an O(n^2 V + n V^2)
precomputation, which is acceptable in settings such as all-pairs adjacency
testing. These results improve upon the more general O(nV) combinatorial and
O(n^3) algebraic adjacency tests from the literature.Comment: 14 pages, 5 figures. v1: published in COCOON 2012. v2: full journal
version, which strengthens and extends the results in Section 2 (see p1 of
the paper for details
Properties and algorithms of the (n, k)-arrangement graphs
The (n, k)-arrangement interconnection topology was first introduced in 1992. The
(n, k )-arrangement graph is a class of generalized star graphs. Compared with the
well known n-star, the (n, k )-arrangement graph is more flexible in degree and diameter.
However, there are few algorithms designed for the (n, k)-arrangement graph
up to present. In this thesis, we will focus on finding graph theoretical properties
of the (n, k)- arrangement graph and developing parallel algorithms that run on this
network.
The topological properties of the arrangement graph are first studied. They include
the cyclic properties. We then study the problems of communication: broadcasting
and routing. Embedding problems are also studied later on. These are very
useful to develop efficient algorithms on this network.
We then study the (n, k )-arrangement network from the algorithmic point of view.
Specifically, we will investigate both fundamental and application algorithms such as
prefix sums computation, sorting, merging and basic geometry computation: finding
convex hull on the (n, k )-arrangement graph.
A literature review of the state-of-the-art in relation to the (n, k)-arrangement
network is also provided, as well as some open problems in this area
Representations of world coordinates in FITS
The initial descriptions of the FITS format provided a simplified method for
describing the physical coordinate values of the image pixels, but deliberately
did not specify any of the detailed conventions required to convey the
complexities of actual image coordinates. Building on conventions in wide use
within astronomy, this paper proposes general extensions to the original
methods for describing the world coordinates of FITS data. In subsequent
papers, we apply these general conventions to the methods by which spherical
coordinates may be projected onto a two-dimensional plane and to
frequency/wavelength/velocity coordinates.Comment: 15 Pages, 1 figure, LaTex with Astronomy & Astrophysics macro
package, submitted to A&A, related papers at
http://www.aoc.nrao.edu/~egreise
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