Abstract: In this paper, a new recursive strategy is proposed for determining $\frac{(n-1)!}{2}$ of $n$th order diagrams. The generalization of $n$th diagram for cross multiplication method were proposed by Pavlovic and Bankier but the specific rule of determining $\frac{(n-1)!}{2}$ of the $n$th order diagrams for square matrix is yet to be discovered. Thus using combinatorial approach, $\frac{(n-1)!}{2}$ of the $n$th order diagrams will be presented as $\frac{(n-1)!}{2}$ starter sets. These starter sets will be generated based on exchanging one element. The advantages of this new strategy are the discarding process was eliminated and the sign of starter set is alternated to each others.
Abstract: If there exists a nonempty, proper subset S of the set of all (n + 1)(n + 2)/2 inertias such that S Ôèå i(A) is sufficient for any n × n zero-nonzero pattern A to be inertially arbitrary, then S is called a critical set of inertias for zero-nonzero patterns of order n. If no proper subset of S is a critical set, then S is called a minimal critical set of inertias. In [3], Kim, Olesky and Driessche identified all minimal critical sets of inertias for 2 × 2 zero-nonzero patterns. Identifying all minimal critical sets of inertias for n × n zero-nonzero patterns with n ≥ 3 is posed as an open question in [3]. In this paper, all minimal critical sets of inertias for 3 × 3 zero-nonzero patterns are identified. It is shown that the sets {(0, 0, 3), (3, 0, 0)}, {(0, 0, 3), (0, 3, 0)}, {(0, 0, 3), (0, 1, 2)}, {(0, 0, 3), (1, 0, 2)}, {(0, 0, 3), (2, 0, 1)} and {(0, 0, 3), (0, 2, 1)} are the only minimal critical sets of inertias for 3 × 3 irreducible zerononzero patterns.
Abstract: In this paper an ant colony optimization algorithm is
developed to solve the permutation flow shop scheduling problem. In
the permutation flow shop scheduling problem which has been vastly
studied in the literature, there are a set of m machines and a set of n
jobs. All the jobs are processed on all the machines and the sequence
of jobs being processed is the same on all the machines. Here this
problem is optimized considering two criteria, makespan and total
flow time. Then the results are compared with the ones obtained by
previously developed algorithms. Finally it is visible that our
proposed approach performs best among all other algorithms in the
literature.
Abstract: This paper presents an approach for repairing word order errors in English text by reordering words in a sentence and choosing the version that maximizes the number of trigram hits according to a language model. A possible way for reordering the words is to use all the permutations. The problem is that for a sentence with length N words the number of all permutations is N!. The novelty of this method concerns the use of an efficient confusion matrix technique for reordering the words. The confusion matrix technique has been designed in order to reduce the search space among permuted sentences. The limitation of search space is succeeded using the statistical inference of N-grams. The results of this technique are very interesting and prove that the number of permuted sentences can be reduced by 98,16%. For experimental purposes a test set of TOEFL sentences was used and the results show that more than 95% can be repaired using the proposed method.
Abstract: A square matrix over the complex field with non- negative integral trace is called a quasi-permutation matrix. For a finite group G the minimal degree of a faithful representation of G by quasi-permutation matrices over the rationals and the complex numbers are denoted by q(G) and c(G) respectively. Finally r (G) denotes the minimal degree of a faithful rational valued complex character of C. The purpose of this paper is to calculate q(G), c(G) and r(G) for the group S L(2, q) when extended by a certain group of order two.
Abstract: Many attempts have been made to strengthen Feistel based block ciphers. Among the successful proposals is the key- dependent S-box which was implemented in some of the high-profile ciphers. In this paper a key-dependent permutation box is proposed and implemented on DES as a case study. The new modified DES, MDES, was tested against Diehard Tests, avalanche test, and performance test. The results showed that in general MDES is more resistible to attacks than DES with negligible overhead. Therefore, it is believed that the proposed key-dependent permutation should be considered as a valuable primitive that can help strengthen the security of Substitution-Permutation Network which is a core design in many Feistel based block ciphers.
Abstract: In cryptography, confusion and diffusion are very
important to get confidentiality and privacy of message in block
ciphers and stream ciphers. There are two types of network to provide
confusion and diffusion properties of message in block ciphers. They
are Substitution- Permutation network (S-P network), and Feistel
network. NLFS (Non-Linear feedback stream cipher) is a fast and
secure stream cipher for software application. NLFS have two modes
basic mode that is synchronous mode and self synchronous mode.
Real random numbers are non-deterministic. R-box (random box)
based on the dynamic properties and it performs the stochastic
transformation of data that can be used effectively meet the
challenges of information is protected from international destructive
impacts. In this paper, a new implementation of stochastic
transformation will be proposed.
Abstract: In this paper, we will generate the wreath product
11 12 M wrM using only two permutations. Also, we will show the
structure of some groups containing the wreath product 11 12 M wrM .
The structure of the groups founded is determined in terms of wreath
product k (M wrM ) wrC 11 12 . Some related cases are also included.
Also, we will show that 132K+1 S and 132K+1 A can be generated
using the wreath product k (M wrM ) wrC 11 12 and a transposition in
132K+1 S and an element of order 3 in 132K+1 A . We will also show
that 132K+1 S and 132K+1 A can be generated using the wreath
product 11 12 M wrM and an element of order k +1.
Abstract: A hardware efficient, multi mode, re-configurable
architecture of interleaver/de-interleaver for multiple standards,
like DVB, WiMAX and WLAN is presented. The interleavers
consume a large part of silicon area when implemented by using
conventional methods as they use memories to store permutation
patterns. In addition, different types of interleavers in different
standards cannot share the hardware due to different construction
methodologies. The novelty of the work presented in this paper is
threefold: 1) Mapping of vital types of interleavers including
convolutional interleaver onto a single architecture with flexibility
to change interleaver size; 2) Hardware complexity for channel
interleaving in WiMAX is reduced by using 2-D realization of the
interleaver functions; and 3) Silicon cost overheads reduced by
avoiding the use of small memories. The proposed architecture
consumes 0.18mm2 silicon area for 0.12μm process and can
operate at a frequency of 140 MHz. The reduced complexity helps
in minimizing the memory utilization, and at the same time
provides strong support to on-the-fly computation of permutation
patterns.
Abstract: The direct implementation of interleaver functions
in WiMAX is not hardware efficient due to presence of complex
functions. Also the conventional method i.e. using memories for
storing the permutation tables is silicon consuming. This work
presents a 2-D transformation for WiMAX channel interleaver
functions which reduces the overall hardware complexity to
compute the interleaver addresses on the fly. A fully reconfigurable
architecture for address generation in WiMAX
channel interleaver is presented, which consume 1.1 k-gates in
total. It can be configured for any block size and any modulation
scheme in WiMAX. The presented architecture can run at a
frequency of 200 MHz, thus fully supporting high bandwidth
requirements for WiMAX.
Abstract: This paper aims to develop an algorithm of finite
capacity material requirement planning (FCMRP) system for a multistage
assembly flow shop. The developed FCMRP system has two
main stages. The first stage is to allocate operations to the first and
second priority work centers and also determine the sequence of the
operations on each work center. The second stage is to determine the
optimal start time of each operation by using a linear programming
model. Real data from a factory is used to analyze and evaluate the
effectiveness of the proposed FCMRP system and also to guarantee a
practical solution to the user. There are five performance measures,
namely, the total tardiness, the number of tardy orders, the total
earliness, the number of early orders, and the average flow-time. The
proposed FCMRP system offers an adjustable solution which is a
compromised solution among the conflicting performance measures.
The user can adjust the weight of each performance measure to
obtain the desired performance. The result shows that the combination
of FCMRP NP3 and EDD outperforms other combinations
in term of overall performance index. The calculation time for the
proposed FCMRP system is about 10 minutes which is practical for
the planners of the factory.
Abstract: Flow-shop scheduling problem (FSP) deals with the
scheduling of a set of jobs that visit a set of machines in the same
order. The FSP is NP-hard, which means that an efficient algorithm
for solving the problem to optimality is unavailable. To meet the
requirements on time and to minimize the make-span performance of
large permutation flow-shop scheduling problems in which there are
sequence dependent setup times on each machine, this paper
develops one hybrid genetic algorithms (HGA). Proposed HGA
apply a modified approach to generate population of initial
chromosomes and also use an improved heuristic called the iterated
swap procedure to improve initial solutions. Also the author uses
three genetic operators to make good new offspring. The results are
compared to some recently developed heuristics and computational
experimental results show that the proposed HGA performs very
competitively with respect to accuracy and efficiency of solution.
Abstract: Artificial Immune System is adopted as a Heuristic
Algorithm to solve the combinatorial problems for decades.
Nevertheless, many of these applications took advantage of the benefit
for applications but seldom proposed approaches for enhancing the
efficiency. In this paper, we continue the previous research to develop
a Self-evolving Artificial Immune System II via coordinating the T
and B cell in Immune System and built a block-based artificial
chromosome for speeding up the computation time and better
performance for different complexities of problems. Through the
design of Plasma cell and clonal selection which are relative the
function of the Immune Response. The Immune Response will help
the AIS have the global and local searching ability and preventing
trapped in local optima. From the experimental result, the significant
performance validates the SEAIS II is effective when solving the
permutation flows-hop problems.
Abstract: This paper presents an improved variable ordering method to obtain the minimum number of nodes in Reduced Ordered Binary Decision Diagrams (ROBDD). The proposed method uses the graph topology to find the best variable ordering. Therefore the input Boolean function is converted to a unidirectional graph. Three levels of graph parameters are used to increase the probability of having a good variable ordering. The initial level uses the total number of nodes (NN) in all the paths, the total number of paths (NP) and the maximum number of nodes among all paths (MNNAP). The second and third levels use two extra parameters: The shortest path among two variables (SP) and the sum of shortest path from one variable to all the other variables (SSP). A permutation of the graph parameters is performed at each level for each variable order and the number of nodes is recorded. Experimental results are promising; the proposed method is found to be more effective in finding the variable ordering for the majority of benchmark circuits.
Abstract: In this researcha particle swarm optimization (PSO)
algorithm is proposedfor no-wait flowshopsequence dependent
setuptime scheduling problem with weighted earliness-tardiness
penalties as the criterion (|,
|Σ
"
).The
smallestposition value (SPV) rule is applied to convert the continuous
value of position vector of particles in PSO to job permutations.A
timing algorithm is generated to find the optimal schedule and
calculate the objective function value of a given sequence in PSO
algorithm. Twodifferent neighborhood structures are applied to
improve the solution quality of PSO algorithm.The first one is based
on variable neighborhood search (VNS) and the second one is a
simple one with invariable structure. In order to compare the
performance of two neighborhood structures, random test problems
are generated and solved by both neighborhood
approaches.Computational results show that the VNS algorithmhas
better performance than the other one especially for the large sized
problems.
Abstract: Star graphs are Cayley graphs of symmetric groups of permutations, with transpositions as the generating sets. A star graph is a preferred interconnection network topology to a hypercube for its ability to connect a greater number of nodes with lower degree. However, an attractive property of the hypercube is that it has a Hamiltonian decomposition, i.e. its edges can be partitioned into disjoint Hamiltonian cycles, and therefore a simple routing can be found in the case of an edge failure. The existence of Hamiltonian cycles in Cayley graphs has been known for some time. So far, there are no published results on the much stronger condition of the existence of Hamiltonian decompositions. In this paper, we give a construction of a Hamiltonian decomposition of the star graph 5-star of degree 4, by defining an automorphism for 5-star and a Hamiltonian cycle which is edge-disjoint with its image under the automorphism.
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 crossed cube is one of the most notable variations of hypercube, but some properties of the former are superior to those of the latter. For example, the diameter of the crossed cube is almost the half of that of the hypercube. In this paper, we focus on the problem embedding a Hamiltonian cycle through an arbitrary given edge in the crossed cube. We give necessary and sufficient condition for determining whether a given permutation with n elements over Zn generates a Hamiltonian cycle pattern of the crossed cube. Moreover, we obtain a lower bound for the number of different Hamiltonian cycles passing through a given edge in an n-dimensional crossed cube. Our work extends some recently obtained results.
Abstract: Independent component analysis (ICA) in the
frequency domain is used for solving the problem of blind source
separation (BSS). However, this method has some problems. For
example, a general ICA algorithm cannot determine the permutation
of signals which is important in the frequency domain ICA. In this
paper, we propose an approach to the solution for a permutation
problem. The idea is to effectively combine two conventional
approaches. This approach improves the signal separation
performance by exploiting features of the conventional approaches.
We show the simulation results using artificial data.
Abstract: Random Forests are a powerful classification technique, consisting of a collection of decision trees. One useful feature of Random Forests is the ability to determine the importance of each variable in predicting the outcome. This is done by permuting each variable and computing the change in prediction accuracy before and after the permutation. This variable importance calculation is similar to a one-factor-at a time experiment and therefore is inefficient. In this paper, we use a regular fractional factorial design to determine which variables to permute. Based on the results of the trials in the experiment, we calculate the individual importance of the variables, with improved precision over the standard method. The method is illustrated with a study of student attrition at Monash University.