Abstract: This research presents the first constant approximation
algorithm to the p-median network design problem with multiple
cable types. This problem was addressed with a single cable type and
there is a bifactor approximation algorithm for the problem. To the
best of our knowledge, the algorithm proposed in this paper is the first
constant approximation algorithm for the p-median network design
with multiple cable types. The addressed problem is a combination of
two well studied problems which are p-median problem and network
design problem. The introduced algorithm is a random sampling
approximation algorithm of constant factor which is conceived by
using some random sampling techniques form the literature. It is
based on a redistribution Lemma from the literature and a steiner tree
problem as a subproblem. This algorithm is simple, and it relies on the
notions of random sampling and probability. The proposed approach
gives an approximation solution with one constant ratio without
violating any of the constraints, in contrast to the one proposed in the
literature. This paper provides a (21 + 2)-approximation algorithm
for the p-median network design problem with multiple cable types
using random sampling techniques.
Abstract: In this paper, a mixed integer linear programming (MILP) model is presented to solve the flexible job shop scheduling problem (FJSP). This problem is one of the hardest combinatorial problems. The objective considered is the minimization of the makespan. The computational results of the proposed MILP model were compared with those of the best known mathematical model in the literature in terms of the computational time. The results show that our model has better performance with respect to all the considered performance measures including relative percentage deviation (RPD) value, number of constraints, and total number of variables. By this improved mathematical model, larger FJS problems can be optimally solved in reasonable time, and therefore, the model would be a better tool for the performance evaluation of the approximation algorithms developed for the problem.
Abstract: We present a robust nonlinear parabolic partial
differential equation (PDE)-based denoising scheme in this article.
Our approach is based on a second-order anisotropic diffusion model
that is described first. Then, a consistent and explicit numerical
approximation algorithm is constructed for this continuous model by
using the finite-difference method. Finally, our restoration
experiments and method comparison, which prove the effectiveness
of this proposed technique, are discussed in this paper.
Abstract: In this paper, we study the Minimum Latency Broadcast
Scheduling (MLBS) problem in wireless sensor networks (WSNs).
The main issue of the MLBS problem is to compute schedules
with the minimum number of timeslots such that a base station can
broadcast data to all other sensor nodes with no collisions. Unlike
existing works that utilize the traditional omni-directional WSNs,
we target the directional WSNs where nodes can collaboratively
determine and orientate their antenna directions. We first develop
a 7-approximation algorithm, adopting directional WSNs. Our ratio
is currently the best, to the best of our knowledge. We then validate
the performance of the proposed algorithm through simulation.
Abstract: In this paper, we study the data collection problem in
Wireless Sensor Networks (WSNs) adopting the two interference
models: The graph model and the more realistic physical interference
model known as Signal-to-Interference-Noise-Ratio (SINR). The
main issue of the problem is to compute schedules with the minimum
number of timeslots, that is, to compute the minimum latency
schedules, such that data from every node can be collected without
any collision or interference to a sink node. While existing works
studied the problem with unit-sized and unbounded-sized message
models, we investigate the problem with the bounded-sized message
model, and introduce a constant factor approximation algorithm.
To the best known of our knowledge, our result is the first result
of the data collection problem with bounded-sized model in both
interference models.
Abstract: The Shortest Approximate Common Superstring
(SACS) problem is : Given a set of strings f={w1, w2, ... , wn},
where no wi is an approximate substring of wj, i ≠ j, find a shortest
string Sa, such that, every string of f is an approximate substring of
Sa. When the number of the strings n>2, the SACS problem becomes
NP-complete. In this paper, we present a greedy approximation
SACS algorithm. Our algorithm is a 1/2-approximation for the SACS
problem. It is of complexity O(n2*(l2+log(n))) in computing time,
where n is the number of the strings and l is the length of a string.
Our SACS algorithm is based on computation of the Length of the
Approximate Longest Overlap (LALO).
Abstract: An exact algorithm for a n-link manipulator movement amidst arbitrary unknown static obstacles is presented.
The algorithm guarantees the reaching of a target configuration of the manipulator in a finite number of steps. The algorithm is
reduced to a finite number of calls of a subroutine for planning a trajectory in the presence of known forbidden states. The polynomial approximation algorithm which is used as the subroutine is presented. The results of the exact algorithm
implementation for the control of a seven link (7 degrees of
freedom, 7DOF) manipulator are given.
Abstract: The Minimum Vertex Cover (MVC) problem is a classic
graph optimization NP - complete problem. In this paper a competent
algorithm, called Vertex Support Algorithm (VSA), is designed to
find the smallest vertex cover of a graph. The VSA is tested on a
large number of random graphs and DIMACS benchmark graphs.
Comparative study of this algorithm with the other existing methods
has been carried out. Extensive simulation results show that the VSA
can yield better solutions than other existing algorithms found in the
literature for solving the minimum vertex cover problem.
Abstract: The Minimum Weighted Vertex Cover (MWVC) problem is a classic graph optimization NP - complete problem. Given an undirected graph G = (V, E) and weighting function defined on the vertex set, the minimum weighted vertex cover problem is to find a vertex set S V whose total weight is minimum subject to every edge of G has at least one end point in S. In this paper an effective algorithm, called Support Ratio Algorithm (SRA), is designed to find the minimum weighted vertex cover of a graph. Computational experiments are designed and conducted to study the performance of our proposed algorithm. Extensive simulation results show that the SRA can yield better solutions than other existing algorithms found in the literature for solving the minimum vertex cover problem.
Abstract: Frequent pattern discovery over data stream is a hard
problem because a continuously generated nature of stream does not
allow a revisit on each data element. Furthermore, pattern discovery
process must be fast to produce timely results. Based on these
requirements, we propose an approximate approach to tackle the
problem of discovering frequent patterns over continuous stream.
Our approximation algorithm is intended to be applied to process a
stream prior to the pattern discovery process. The results of
approximate frequent pattern discovery have been reported in the
paper.
Abstract: The algorithms of convex hull have been extensively studied in literature, principally because of their wide range of applications in different areas. This article presents an efficient algorithm to construct approximate convex hull from a set of n points in the plane in O(n + k) time, where k is the approximation error control parameter. The proposed algorithm is suitable for applications preferred to reduce the computation time in exchange of accuracy level such as animation and interaction in computer graphics where rapid and real-time graphics rendering is indispensable.
Abstract: The Block Sorting problem is to sort a given
permutation moving blocks. A block is defined as a substring
of the given permutation, which is also a substring of the
identity permutation. Block Sorting has been proved to be
NP-Hard. Until now two different 2-Approximation algorithms
have been presented for block sorting. These are the best known
algorithms for Block Sorting till date. In this work we present
a different characterization of Block Sorting in terms of a
transposition cycle graph. Then we suggest a heuristic,
which we show to exhibit a 2-approximation performance
guarantee for most permutations.
Abstract: The solvated electron is self-trapped (polaron) owing
to strong interaction with the quantum polarization field. If the
electron and quantum field are strongly coupled then the collective
localized state of the field and quasi-particle is formed. In such a
formation the electron motion is rather intricate. On the one hand the
electron oscillated within a rather deep polarization potential well
and undergoes the optical transitions, and on the other, it moves
together with the center of inertia of the system and participates in
the thermal random walk. The problem is to separate these motions
correctly, rigorously taking into account the conservation laws. This
can be conveniently done using Bogolyubov-Tyablikov method of
canonical transformation to the collective coordinates. This
transformation removes the translational degeneracy and allows one
to develop the successive approximation algorithm for the energy and
wave function while simultaneously fulfilling the law of conservation
of total momentum of the system. The resulting equations determine
the electron transitions and depend explicitly on the translational
velocity of the quasi-particle as whole. The frequency of optical
transition is calculated for the solvated electron in ammonia, and an
estimate is made for the thermal-induced spectral bandwidth.
Abstract: The Algorithm 2 for a n-link manipulator movement amidst arbitrary unknown static obstacles for a case when a sensor system supplies information about local neighborhoods of different points in the configuration space is presented. The Algorithm 2 guarantees the reaching of a target position in a finite number of steps. The Algorithm 2 is reduced to a finite number of calls of a subroutine for planning a trajectory in the presence of known forbidden states. The polynomial approximation algorithm which is used as the subroutine is presented. The results of the Algorithm2 implementation are given.