12,277 research outputs found
Optimal parallel algorithms for rectilinear link-distance problems
We provide optimal parallel solutions to several link-distance problems set in trapezoided rectilinear polygons. All our main parallel algorithms are deterministic and designed to run on the exclusive read exclusive write parallel random access machine (EREW PRAM). Let P be a trapezoided rectilinear simple polygon with n vertices. In O(log n) time using O(n/log n) processors we can optimally compute: 1. Minimum réctilinear link paths, or shortest paths in the L1 metric from any point in P to all vertices of P. 2. Minimum rectilinear link paths from any segment inside P to all vertices of P. 3. The rectilinear window (histogram) partition of P. 4. Both covering radii and vertex intervals for any diagonal of P. 5. A data structure to support rectilinear link-distance queries between any two points in P (queries can be answered optimally in O(log n) time by uniprocessor). Our solution to 5 is based on a new linear-time sequential algorithm for this problem which is also provided here. This improves on the previously best-known sequential algorithm for this problem which used O(n log n) time and space.5 We develop techniques for solving link-distance problems in parallel which are expected to find applications in the design of other parallel computational geometry algorithms. We employ these parallel techniques, for example, to compute (on a CREW PRAM) optimally the link diameter, the link center, and the central diagonal of a rectilinear polygon
Rectilinear Link Diameter and Radius in a Rectilinear Polygonal Domain
We study the computation of the diameter and radius under the rectilinear
link distance within a rectilinear polygonal domain of vertices and
holes. We introduce a \emph{graph of oriented distances} to encode the distance
between pairs of points of the domain. This helps us transform the problem so
that we can search through the candidates more efficiently. Our algorithm
computes both the diameter and the radius in time, where denotes the matrix
multiplication exponent and is the number of
edges of the graph of oriented distances. We also provide a faster algorithm
for computing the diameter that runs in time
Ramified rectilinear polygons: coordinatization by dendrons
Simple rectilinear polygons (i.e. rectilinear polygons without holes or
cutpoints) can be regarded as finite rectangular cell complexes coordinatized
by two finite dendrons. The intrinsic -metric is thus inherited from the
product of the two finite dendrons via an isometric embedding. The rectangular
cell complexes that share this same embedding property are called ramified
rectilinear polygons. The links of vertices in these cell complexes may be
arbitrary bipartite graphs, in contrast to simple rectilinear polygons where
the links of points are either 4-cycles or paths of length at most 3. Ramified
rectilinear polygons are particular instances of rectangular complexes obtained
from cube-free median graphs, or equivalently simply connected rectangular
complexes with triangle-free links. The underlying graphs of finite ramified
rectilinear polygons can be recognized among graphs in linear time by a
Lexicographic Breadth-First-Search. Whereas the symmetry of a simple
rectilinear polygon is very restricted (with automorphism group being a
subgroup of the dihedral group ), ramified rectilinear polygons are
universal: every finite group is the automorphism group of some ramified
rectilinear polygon.Comment: 27 pages, 6 figure
Key distribution in PKC through Quantas
Cryptography literally means "The art & science of secret writing & sending a
message between two parties in such a way that its contents cannot be
understood by someone other than the intended recipient". and Quantum word is
related with "Light". Thus, Quantum Cryptography is a way of descripting any
information in the form of quantum particles. There are no classical
cryptographic systems which are perfectly secure. In contrast to Classical
cryptography which depends upon Mathematics, Quantum Cryptography utilizes the
concepts of Quantum Physics which provides us the security against the
cleverest marauders of the present age. In the view of increasing need of
Network and Information Security, we do require methods to overcome the
Molecular Computing technologies (A future technology) and other techniques of
the various codebrakers. Both the parts i.e. Quantum Key distribution and
Information transference from Sender to Receiver are much efficient and secure.
It is based upon BB84 protocol. It can be of great use for Govt. agencies such
as Banks, Insurance, Brokerages firms, financial institutions, e-commerce and
most important is the Defense & security of any country. It is a Cryptographic
communication system in which the original users can detect unauthorized
eavesdropper and in addition it gives a guarantee of no eavesdropping. It
proves to be the ultra secure mode of communication b/w two intended parties.Comment: 11 Pages, JGraph-Hoc Journal 201
Covering Points by Disjoint Boxes with Outliers
For a set of n points in the plane, we consider the axis--aligned (p,k)-Box
Covering problem: Find p axis-aligned, pairwise-disjoint boxes that together
contain n-k points. In this paper, we consider the boxes to be either squares
or rectangles, and we want to minimize the area of the largest box. For general
p we show that the problem is NP-hard for both squares and rectangles. For a
small, fixed number p, we give algorithms that find the solution in the
following running times:
For squares we have O(n+k log k) time for p=1, and O(n log n+k^p log^p k time
for p = 2,3. For rectangles we get O(n + k^3) for p = 1 and O(n log n+k^{2+p}
log^{p-1} k) time for p = 2,3.
In all cases, our algorithms use O(n) space.Comment: updated version: - changed problem from 'cover exactly n-k points' to
'cover at least n-k points' to avoid having non-feasible solutions. Results
are unchanged. - added Proof to Lemma 11, clarified some sections - corrected
typos and small errors - updated affiliations of two author
Realization of Reverse Motion of the Model of a Semitrailer Road Train
The complexity of controlling the road train is due to pronounced nonlinearities, as well as the instability of the control object under reverse motion, often leading to a phenomenon known as jackknifing. Because of this, the task of controlling their motion is relevant, both from the theoretical point of view and from the point of view of the practical implementation of software motion with given constraints.The task of controlling the motion of a road train with a semitrailer under the assumption of non-holonomic constraints (the absence of lateral slippage of support wheels) has a great theoretical and applied significance. Research in this field is stimulated by numerous applied problems.For road trains, the location of the towing device behind the rear axle (off-axle hitching model) is quite typical. This model is used in this study. For this model, management and planning methods are proposed, using a diverse mathematical apparatus. Among the most frequently used methods, let's select the methods of feedback linearization and chain systems, and methods are used, which are exclusively due to the geometric features of the model kinematics formulated in cascade form. Synthesis of control laws can be performed after the linearization of the model by state feedback, using the Lie algebra apparatus, fuzzy logic, using linear-quadratic controllers, nilpotent approximation, and so on.Studies have been carried out on the state of solving the problem associated with the reverse motion of a road train consisting of a hauler and a semitrailer with a coupling sideshift. The synthesized stabilizing control allowed to study the features of such model, determined by its linear dimensions and dynamic parameters.In this study, one of the possibilities of stabilizing the reversal motion of the dynamic model of a two-link road train on a rectilinear and circular track is considered. Synthesis of the stabilizing control is obtained for the case of rectilinear motion, hauler, stable circular stationary regimes are realized. The obtained theoretical relationships that determine the properties of the crew's ability to rotate when moving in reverse, allow the latter to be used when the algorithm is implemented
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