5,565 research outputs found
Finding approximate palindromes in strings
We introduce a novel definition of approximate palindromes in strings, and
provide an algorithm to find all maximal approximate palindromes in a string
with up to errors. Our definition is based on the usual edit operations of
approximate pattern matching, and the algorithm we give, for a string of size
on a fixed alphabet, runs in time. We also discuss two
implementation-related improvements to the algorithm, and demonstrate their
efficacy in practice by means of both experiments and an average-case analysis
Cellular Automata Applications in Shortest Path Problem
Cellular Automata (CAs) are computational models that can capture the
essential features of systems in which global behavior emerges from the
collective effect of simple components, which interact locally. During the last
decades, CAs have been extensively used for mimicking several natural processes
and systems to find fine solutions in many complex hard to solve computer
science and engineering problems. Among them, the shortest path problem is one
of the most pronounced and highly studied problems that scientists have been
trying to tackle by using a plethora of methodologies and even unconventional
approaches. The proposed solutions are mainly justified by their ability to
provide a correct solution in a better time complexity than the renowned
Dijkstra's algorithm. Although there is a wide variety regarding the
algorithmic complexity of the algorithms suggested, spanning from simplistic
graph traversal algorithms to complex nature inspired and bio-mimicking
algorithms, in this chapter we focus on the successful application of CAs to
shortest path problem as found in various diverse disciplines like computer
science, swarm robotics, computer networks, decision science and biomimicking
of biological organisms' behaviour. In particular, an introduction on the first
CA-based algorithm tackling the shortest path problem is provided in detail.
After the short presentation of shortest path algorithms arriving from the
relaxization of the CAs principles, the application of the CA-based shortest
path definition on the coordinated motion of swarm robotics is also introduced.
Moreover, the CA based application of shortest path finding in computer
networks is presented in brief. Finally, a CA that models exactly the behavior
of a biological organism, namely the Physarum's behavior, finding the
minimum-length path between two points in a labyrinth is given.Comment: To appear in the book: Adamatzky, A (Ed.) Shortest path solvers. From
software to wetware. Springer, 201
On the Greedy Algorithm for the Shortest Common Superstring Problem with Reversals
We study a variation of the classical Shortest Common Superstring (SCS)
problem in which a shortest superstring of a finite set of strings is
sought containing as a factor every string of or its reversal. We call this
problem Shortest Common Superstring with Reversals (SCS-R). This problem has
been introduced by Jiang et al., who designed a greedy-like algorithm with
length approximation ratio . In this paper, we show that a natural
adaptation of the classical greedy algorithm for SCS has (optimal) compression
ratio , i.e., the sum of the overlaps in the output string is at least
half the sum of the overlaps in an optimal solution. We also provide a
linear-time implementation of our algorithm.Comment: Published in Information Processing Letter
A Fast Algorithm Finding the Shortest Reset Words
In this paper we present a new fast algorithm finding minimal reset words for
finite synchronizing automata. The problem is know to be computationally hard,
and our algorithm is exponential. Yet, it is faster than the algorithms used so
far and it works well in practice. The main idea is to use a bidirectional BFS
and radix (Patricia) tries to store and compare resulted subsets. We give both
theoretical and practical arguments showing that the branching factor is
reduced efficiently. As a practical test we perform an experimental study of
the length of the shortest reset word for random automata with states and 2
input letters. We follow Skvorsov and Tipikin, who have performed such a study
using a SAT solver and considering automata up to states. With our
algorithm we are able to consider much larger sample of automata with up to
states. In particular, we obtain a new more precise estimation of the
expected length of the shortest reset word .Comment: COCOON 2013. The final publication is available at
http://link.springer.com/chapter/10.1007%2F978-3-642-38768-5_1
- …