4 research outputs found
Finding the Anticover of a String
A k-anticover of a string x is a set of pairwise distinct factors of x of equal length k, such that every symbol of x is contained into an occurrence of at least one of those factors. The existence of a k-anticover can be seen as a notion of non-redundancy, which has application in computational biology, where they are associated with various non-regulatory mechanisms. In this paper we address the complexity of the problem of finding a k-anticover of a string x if it exists, showing that the decision problem is NP-complete on general strings for k ? 3. We also show that the problem admits a polynomial-time solution for k=2. For unbounded k, we provide an exact exponential algorithm to find a k-anticover of a string of length n (or determine that none exists), which runs in O*(min {3^{(n-k)/3)}, ((k(k+1))/2)^{n/(k+1)) time using polynomial space
Finding the Anticover of a String
A k-anticover of a string x is a set of pairwise distinct factors of x of equal length k, such that every symbol of x is contained into an occurrence of at least one of those factors. The existence of a k-anticover can be seen as a notion of non-redundancy, which has application in computational biology, where they are associated with various non-regulatory mechanisms. In this paper we address the complexity of the problem of finding a k-anticover of a string x if it exists, showing that the decision problem is NP-complete on general strings for k-3. We also show that the problem admits a polynomial-time solution for k = 2. For unbounded k, we provide an exact exponential algorithm to find a k-anticover of a string of length n (or determine that none exists), which runs in O(min{3 n-k 3 , ( k(k+1) 2 ) n k+1 }) time using polynomial space. 2012 ACM Subject Classification Mathematics of computing ! Combinatorics on words
String Covering: A Survey
The study of strings is an important combinatorial field that precedes the
digital computer. Strings can be very long, trillions of letters, so it is
important to find compact representations. Here we first survey various forms
of one potential compaction methodology, the cover of a given string x,
initially proposed in a simple form in 1990, but increasingly of interest as
more sophisticated variants have been discovered. We then consider covering by
a seed; that is, a cover of a superstring of x. We conclude with many proposals
for research directions that could make significant contributions to string
processing in future
Problemas de localização-distribuição de serviços semiobnóxios: aproximações e apoio à decisão
Doutoramento em Gestão IndustrialA presente tese resulta de um trabalho de investigação cujo objectivo se
centrou no problema de localização-distribuição (PLD) que pretende abordar,
de forma integrada, duas actividades logÃsticas intimamente relacionadas: a
localização de equipamentos e a distribuição de produtos.
O PLD, nomeadamente a sua modelação matemática, tem sido estudado na
literatura, dando origem a diversas aproximações que resultam de diferentes
cenários reais. Importa portanto agrupar as diferentes variantes por forma a
facilitar e potenciar a sua investigação. Após fazer uma revisão e propor uma
taxonomia dos modelos de localização-distribuição, este trabalho foca-se na
resolução de alguns modelos considerados como mais representativos. É feita
assim a análise de dois dos PLDs mais básicos (os problema capacitados com
procura nos nós e nos arcos), sendo apresentadas, para ambos, propostas de
resolução. Posteriormente, é abordada a localização-distribuição de serviços
semiobnóxios. Este tipo de serviços, ainda que seja necessário e
indispensável para o público em geral, dada a sua natureza, exerce um efeito
desagradável sobre as comunidades contÃguas. Assim, aos critérios
tipicamente utilizados na tomada de decisão sobre a localização destes
serviços (habitualmente a minimização de custo) é necessário adicionar
preocupações que reflectem a manutenção da qualidade de vida das regiões
que sofrem o impacto do resultado da referida decisão.
A abordagem da localização-distribuição de serviços semiobnóxios requer
portanto uma análise multi-objectivo. Esta análise pode ser feita com recurso a
dois métodos distintos: não interactivos e interactivos. Ambos são abordados
nesta tese, com novas propostas, sendo o método interactivo proposto
aplicável a outros problemas de programação inteira mista multi-objectivo.
Por último, é desenvolvida uma ferramenta de apoio à decisão para os
problemas abordados nesta tese, sendo apresentada a metodologia adoptada
e as suas principais funcionalidades. A ferramenta desenvolvida tem grandes
preocupações com a interface de utilizador, visto ser direccionada para
decisores que tipicamente não têm conhecimentos sobre os modelos
matemáticos subjacentes a este tipo de problemas.This thesis main objective is to address the location-routing problem (LRP)
which intends to tackle, using an integrated approach, two highly related
logistics activities: the location of facilities and the distribution of materials.
The LRP, namely its mathematical formulation, has been studied in the
literature, and several approaches have emerged, corresponding to different
real-world scenarios. Therefore, it is important to identify and group the
different LRP variants, in order to segment current research and foster future
studies. After presenting a review and a taxonomy of location-routing models,
the following research focuses on solving some of its variants. Thus, a study of
two of the most basic LRPs (capacitated problems with demand either on the
nodes or on the arcs) is performed, and new approaches are presented.
Afterwards, the location-routing of semi-obnoxious facilities is addressed.
These are facilities that, although providing useful and indispensible services,
given their nature, bring about an undesirable effect to adjacent communities.
Consequently, to the usual objectives when considering their location (cost
minimization), new ones must be added that are able to reflect concerns
regarding the quality of life of the communities impacted by the outcome of
these decisions.
The location-routing of semi-obnoxious facilities therefore requires to be
analysed using multi-objective approaches, which can be of two types: noninteractive
or interactive. Both are discussed and new methods proposed in this
thesis; the proposed interactive method is suitable to other multi-objective
mixed integer programming problems.
Finally, a newly developed decision-support tool to address the LRP is
presented (being the adopted methodology discussed, and its main
functionalities shown). This tool has great concerns regarding the user
interface, as it is directed at decision makers who typically don’t have specific
knowledge of the underlying models of this type of problems