1,017 research outputs found
A Minimal Periods Algorithm with Applications
Kosaraju in ``Computation of squares in a string'' briefly described a
linear-time algorithm for computing the minimal squares starting at each
position in a word. Using the same construction of suffix trees, we generalize
his result and describe in detail how to compute in O(k|w|)-time the minimal
k-th power, with period of length larger than s, starting at each position in a
word w for arbitrary exponent and integer . We provide the
complete proof of correctness of the algorithm, which is somehow not completely
clear in Kosaraju's original paper. The algorithm can be used as a sub-routine
to detect certain types of pseudo-patterns in words, which is our original
intention to study the generalization.Comment: 14 page
The stochastic matching problem
The matching problem plays a basic role in combinatorial optimization and in
statistical mechanics. In its stochastic variants, optimization decisions have
to be taken given only some probabilistic information about the instance. While
the deterministic case can be solved in polynomial time, stochastic variants
are worst-case intractable. We propose an efficient method to solve stochastic
matching problems which combines some features of the survey propagation
equations and of the cavity method. We test it on random bipartite graphs, for
which we analyze the phase diagram and compare the results with exact bounds.
Our approach is shown numerically to be effective on the full range of
parameters, and to outperform state-of-the-art methods. Finally we discuss how
the method can be generalized to other problems of optimization under
uncertainty.Comment: Published version has very minor change
Construct, Merge, Solve and Adapt: Application to the repetition-free longest common subsequence problem
In this paper we present the application of a recently proposed, general, algorithm for combinatorial optimization to the repetition-free longest common subsequence problem. The applied algorithm, which is labelled Construct, Merge, Solve & Adapt, generates sub-instances based on merging the solution components found in randomly constructed solutions. These sub-instances are subsequently solved by means of an exact solver. Moreover, the considered sub-instances are dynamically changing due to adding new solution components at each iteration, and removing existing solution components on the basis of indicators about their usefulness. The results of applying this algorithm to the repetition-free longest common subsequence problem show that the algorithm generally outperforms competing approaches from the literature. Moreover, they show that the algorithm is competitive with CPLEX for small and medium size problem instances, whereas it outperforms CPLEX for larger problem instances.Peer ReviewedPostprint (author's final draft
Wave Energy: a Pacific Perspective
This is the author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by The Royal Society and can be found at: http://rsta.royalsocietypublishing.org/.This paper illustrates the status of wave energy development in Pacific Rim countries by characterizing the available resource and introducing the region‟s current and potential future leaders in wave energy converter development. It also describes the existing licensing and permitting process as well as potential environmental concerns. Capabilities of Pacific Ocean testing facilities are described in addition to the region‟s vision of the future of wave energy
On the maximal sum of exponents of runs in a string
A run is an inclusion maximal occurrence in a string (as a subinterval) of a
repetition with a period such that . The exponent of a run
is defined as and is . We show new bounds on the maximal sum of
exponents of runs in a string of length . Our upper bound of is
better than the best previously known proven bound of by Crochemore &
Ilie (2008). The lower bound of , obtained using a family of binary
words, contradicts the conjecture of Kolpakov & Kucherov (1999) that the
maximal sum of exponents of runs in a string of length is smaller than Comment: 7 pages, 1 figur
Scheduling Jobs in Flowshops with the Introduction of Additional Machines in the Future
This is the author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Elsevier and can be found at: http://www.journals.elsevier.com/expert-systems-with-applications/.The problem of scheduling jobs to minimize total weighted tardiness in flowshops,\ud
with the possibility of evolving into hybrid flowshops in the future, is investigated in\ud
this paper. As this research is guided by a real problem in industry, the flowshop\ud
considered has considerable flexibility, which stimulated the development of an\ud
innovative methodology for this research. Each stage of the flowshop currently has\ud
one or several identical machines. However, the manufacturing company is planning\ud
to introduce additional machines with different capabilities in different stages in the\ud
near future. Thus, the algorithm proposed and developed for the problem is not only\ud
capable of solving the current flow line configuration but also the potential new\ud
configurations that may result in the future. A meta-heuristic search algorithm based\ud
on Tabu search is developed to solve this NP-hard, industry-guided problem. Six\ud
different initial solution finding mechanisms are proposed. A carefully planned\ud
nested split-plot design is performed to test the significance of different factors and\ud
their impact on the performance of the different algorithms. To the best of our\ud
knowledge, this research is the first of its kind that attempts to solve an industry-guided\ud
problem with the concern for future developments
Searching of gapped repeats and subrepetitions in a word
A gapped repeat is a factor of the form where and are nonempty
words. The period of the gapped repeat is defined as . The gapped
repeat is maximal if it cannot be extended to the left or to the right by at
least one letter with preserving its period. The gapped repeat is called
-gapped if its period is not greater than . A
-subrepetition is a factor which exponent is less than 2 but is not
less than (the exponent of the factor is the quotient of the length
and the minimal period of the factor). The -subrepetition is maximal if
it cannot be extended to the left or to the right by at least one letter with
preserving its minimal period. We reveal a close relation between maximal
gapped repeats and maximal subrepetitions. Moreover, we show that in a word of
length the number of maximal -gapped repeats is bounded by
and the number of maximal -subrepetitions is bounded by
. Using the obtained upper bounds, we propose algorithms for
finding all maximal -gapped repeats and all maximal
-subrepetitions in a word of length . The algorithm for finding all
maximal -gapped repeats has time complexity for the case
of constant alphabet size and time complexity for the
general case. For finding all maximal -subrepetitions we propose two
algorithms. The first algorithm has time
complexity for the case of constant alphabet size and time complexity for the general case. The
second algorithm has
expected time complexity
Duel and sweep algorithm for order-preserving pattern matching
Given a text and a pattern over alphabet , the classic exact
matching problem searches for all occurrences of pattern in text .
Unlike exact matching problem, order-preserving pattern matching (OPPM)
considers the relative order of elements, rather than their real values. In
this paper, we propose an efficient algorithm for OPPM problem using the
"duel-and-sweep" paradigm. Our algorithm runs in time in
general and time under an assumption that the characters in a string
can be sorted in linear time with respect to the string size. We also perform
experiments and show that our algorithm is faster that KMP-based algorithm.
Last, we introduce the two-dimensional order preserved pattern matching and
give a duel and sweep algorithm that runs in time for duel stage and
time for sweeping time with preprocessing time.Comment: 13 pages, 5 figure
Bethe Ansatz in the Bernoulli Matching Model of Random Sequence Alignment
For the Bernoulli Matching model of sequence alignment problem we apply the
Bethe ansatz technique via an exact mapping to the 5--vertex model on a square
lattice. Considering the terrace--like representation of the sequence alignment
problem, we reproduce by the Bethe ansatz the results for the averaged length
of the Longest Common Subsequence in Bernoulli approximation. In addition, we
compute the average number of nucleation centers of the terraces.Comment: 14 pages, 5 figures (some points are clarified
Two algorithms for the student-project allocation problem
We study the Student-Project Allocation problem (SPA), a generalisation of the classical Hospitals / Residents problem (HR). An instance of SPA involves a set of students, projects and lecturers. Each project is offered by a unique lecturer, and both projects and lecturers have capacity constraints. Students have preferences over projects, whilst lecturers have preferences over students. We present two optimal linear-time algorithms for allocating students to projects, subject to the preference and capacity constraints. In particular, each algorithm finds a stable matching of students to projects. Here, the concept of stability generalises the stability definition in the HR context. The stable matching produced by the first algorithm is simultaneously best-possible for all students, whilst the one produced by the second algorithm is simultaneously best-possible for all lecturers. We also prove some structural results concerning the set of stable matchings in a given instance of SPA. The SPA problem model that we consider is very general and has applications to a range of different contexts besides student-project allocation
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