Search results for "combinatoric"
showing 10 items of 1776 documents
The S-kernel: A measure of symmetry of objects
2007
In this paper we introduce a new symmetry feature named ''symmetry kernel'' (SK) to support a measure of symmetry. Given any symmetry transform S, SK of a pattern P is the maximal included symmetric sub-set of P for all directions and shifts. We provide a first algorithm to exhibit this kernel where the centre of symmetry is assumed to be the centre of mass. Then we prove that, in any direction, the optimal axis corresponds to the maximal correlation of a pattern with its symmetric version. That leads to a second algorithm. The associated symmetry measure is a modified difference between the respective surfaces of a pattern and its kernel. A series of experiments supports the actual algorit…
Systems of quasilinear elliptic equations with dependence on the gradient via subsolution-supersolution method
2017
For the homogeneous Dirichlet problem involving a system of equations driven by \begin{document}$(p,q)$\end{document} -Laplacian operators and general gradient dependence we prove the existence of solutions in the ordered rectangle determined by a subsolution-supersolution. This extends the preceding results based on the method of subsolution-supersolution for systems of elliptic equations. Positive and negative solutions are obtained.
Formulations and valid inequalities for the capacitated dispersion problem
2023
This work focuses on the capacitated dispersion problem for which we study several mathematical formulations in different spaces using variables associated with nodes, edges, and costs. The relationships among the presented formulations are investigated by comparing the projections of the feasible sets of the LP relaxations onto the subspace of natural variables. These formulations are then strengthened with families of valid inequalities and variable-fixing procedures. The separation problems associated with the valid inequalities that are exponential in number are shown to be polynomially solvable by reducing them to longest path problems in acyclic graphs. The dual bounds obtained from s…
Design of temperature control system using conventional PID and Intelligent Fuzzy Logic controller
2015
In this paper, we present the design of temperature control for industrial heat treating furnace by using Intelligent Fuzzy Logic and PID controllers. Temperature control is important in heating processes as it can disqualify materials in terms of their physical properties when not well performed. Obviously PID temperature controller is the most used in industries to control non-linear processes. Consequently, it has been found that the output response from Fuzzy Logic is very accurate in terms of overshoot and steady state error when compared to that of PID. Moreover, both temperature controllers are modeled and simulated using MATLAB software.
A loop-free two-close Gray-code algorithm for listing k-ary Dyck words
2006
AbstractP. Chase and F. Ruskey each published a Gray code for length n binary strings with m occurrences of 1, coding m-combinations of n objects, which is two-close—that is, in passing from one binary string to its successor a single 1 exchanges positions with a 0 which is either adjacent to the 1 or separated from it by a single 0. If we impose the restriction that any suffix of a string contains at least k−1 times as many 0's as 1's, we obtain k-suffixes: suffixes of k-ary Dyck words. Combinations are retrieved as special case by setting k=1 and k-ary Dyck words are retrieved as a special case by imposing the additional condition that the entire string has exactly k−1 times as many 0's a…
On parsing optimality for dictionary-based text compression—the Zip case
2013
Dictionary-based compression schemes are the most commonly used data compression schemes since they appeared in the foundational paper of Ziv and Lempel in 1977, and generally referred to as LZ77. Their work is the base of Zip, gZip, 7-Zip and many other compression software utilities. Some of these compression schemes use variants of the greedy approach to parse the text into dictionary phrases; others have left the greedy approach to improve the compression ratio. Recently, two bit-optimal parsing algorithms have been presented filling the gap between theory and best practice. We present a survey on the parsing problem for dictionary-based text compression, identifying noticeable results …
Dictionary-symbolwise flexible parsing
2012
AbstractLinear-time optimal parsing algorithms are rare in the dictionary-based branch of the data compression theory. A recent result is the Flexible Parsing algorithm of Matias and Sahinalp (1999) that works when the dictionary is prefix closed and the encoding of dictionary pointers has a constant cost. We present the Dictionary-Symbolwise Flexible Parsing algorithm that is optimal for prefix-closed dictionaries and any symbolwise compressor under some natural hypothesis. In the case of LZ78-like algorithms with variable costs and any, linear as usual, symbolwise compressor we show how to implement our parsing algorithm in linear time. In the case of LZ77-like dictionaries and any symbol…
A Logical Key Hierarchy Based approach to preserve content privacy in Decentralized Online Social Networks
2020
Distributed Online Social Networks (DOSNs) have been proposed to shift the control over user data from a unique entity, the online social network provider, to the users of the DOSN themselves. In this paper we focus on the problem of preserving the privacy of the contents shared to large groups of users. In general, content privacy is enforced by encrypting the content, having only authorized parties being able to decrypt it. When efficiency has to be taken into account, new solutions have to be devised that: i) minimize the re-encryption of the contents published in a group when the composition of the group changes; and, ii) enable a fast distribution of the cryptographic keys to all the m…
The Burrows-Wheeler Transform between Data Compression and Combinatorics on Words
2013
The Burrows-Wheeler Transform (BWT) is a tool of fundamental importance in Data Compression and, recently, has found many applications well beyond its original purpose. The main goal of this paper is to highlight the mathematical and combinatorial properties on which the outstanding versatility of the $BWT$ is based, i.e. its reversibility and the clustering effect on the output. Such properties have aroused curiosity and fervent interest in the scientific world both for theoretical aspects and for practical effects. In particular, in this paper we are interested both to survey the theoretical research issues which, by taking their cue from Data Compression, have been developed in the conte…
Automata and forbidden words
1998
Abstract Let L ( M ) be the (factorial) language avoiding a given anti-factorial language M . We design an automaton accepting L ( M ) and built from the language M . The construction is effective if M is finite. If M is the set of minimal forbidden words of a single word ν, the automaton turns out to be the factor automaton of ν (the minimal automaton accepting the set of factors of ν). We also give an algorithm that builds the trie of M from the factor automaton of a single word. It yields a nontrivial upper bound on the number of minimal forbidden words of a word.