3,548 research outputs found
Online Abelian Pattern Matching
Ejaz T, Rahmann S, Stoye J. Online Abelian Pattern Matching. Forschungsberichte der Technischen Fakultät, Abteilung Informationstechnik / Universität Bielefeld. Bielefeld: Technische Fakultät der Universität Bielefeld; 2008.An abelian pattern describes the set of strings that comprise of the same combination of characters. Given an abelian pattern P and a text T [Epsilon] [Sigma]^n, the task is to find all occurrences of P in T, i.e. all substrings S = T_i...T_j such that the frequency of each character in S matches the specified frequency of that character in P.
In this report we present simple online algorithms for abelian pattern matching, and give a lower bound for online algorithms which is [Omega](n)
On the Parikh-de-Bruijn grid
We introduce the Parikh-de-Bruijn grid, a graph whose vertices are
fixed-order Parikh vectors, and whose edges are given by a simple shift
operation. This graph gives structural insight into the nature of sets of
Parikh vectors as well as that of the Parikh set of a given string. We show its
utility by proving some results on Parikh-de-Bruijn strings, the abelian analog
of de-Bruijn sequences.Comment: 18 pages, 3 figures, 1 tabl
Identifying all abelian periods of a string in quadratic time and relevant problems
Abelian periodicity of strings has been studied extensively over the last
years. In 2006 Constantinescu and Ilie defined the abelian period of a string
and several algorithms for the computation of all abelian periods of a string
were given. In contrast to the classical period of a word, its abelian version
is more flexible, factors of the word are considered the same under any
internal permutation of their letters. We show two O(|y|^2) algorithms for the
computation of all abelian periods of a string y. The first one maps each
letter to a suitable number such that each factor of the string can be
identified by the unique sum of the numbers corresponding to its letters and
hence abelian periods can be identified easily. The other one maps each letter
to a prime number such that each factor of the string can be identified by the
unique product of the numbers corresponding to its letters and so abelian
periods can be identified easily. We also define weak abelian periods on
strings and give an O(|y|log(|y|)) algorithm for their computation, together
with some other algorithms for more basic problems.Comment: Accepted in the "International Journal of foundations of Computer
Science
Algorithms for Computing Abelian Periods of Words
Constantinescu and Ilie (Bulletin EATCS 89, 167--170, 2006) introduced the
notion of an \emph{Abelian period} of a word. A word of length over an
alphabet of size can have distinct Abelian periods.
The Brute-Force algorithm computes all the Abelian periods of a word in time
using space. We present an off-line
algorithm based on a \sel function having the same worst-case theoretical
complexity as the Brute-Force one, but outperforming it in practice. We then
present on-line algorithms that also enable to compute all the Abelian periods
of all the prefixes of .Comment: Accepted for publication in Discrete Applied Mathematic
Confinement in N=1 SQCD: One Step Beyond Seiberg's Duality
We consider N=1 supersymmetric quantum chromodynamics (SQCD) with the gauge
group U(N_c) and N_c+N quark flavors. N_c flavors are massless; the
corresponding squark fields develop (small) vacuum expectation values (VEVs) on
the Higgs branch. Extra N flavors are endowed with small (and equal) mass
terms. We study this theory through its Seiberg's dual: U(N) gauge theory with
N_c +N flavors of "dual quark" fields plus a gauge-singlet mesonic field M. The
original theory is referred to as "quark theory" while the dual one is termed
"monopole theory." The suggested mild deformation of Seiberg's procedure
changes the dynamical regime of the monopole theory from infrared free to
asymptotically free at large distances. We show that, upon condensation of the
"dual quarks," the dual theory supports non-Abelian flux tubes (strings).
Seiberg's duality is extended beyond purely massless states to include light
states on both sides. Being interpreted in terms of the quark theory, the
monopole-theory flux tubes are supposed to carry chromoelectric fields. The
string junctions -- confined monopole-theory monopoles -- can be viewed as
"constituent quarks" of the original quark theory. We interpret closed strings
as glueballs of the original quark theory. Moreover, there are string
configurations formed by two junctions connected by a pair of different
non-Abelian strings. These can be considered as constituent quark mesons of the
quark theory.Comment: 30 pages, 3 figures; v2 a reference added, minor comments added;
final version to be published in PR
Quantum pattern matching fast on average
The -dimensional pattern matching problem is to find an occurrence of a
pattern of length within a text of length , with . This task models various problems in text and
image processing, among other application areas. This work describes a quantum
algorithm which solves the pattern matching problem for random patterns and
texts in time . For
large this is super-polynomially faster than the best possible classical
algorithm, which requires time . The
algorithm is based on the use of a quantum subroutine for finding hidden shifts
in dimensions, which is a variant of algorithms proposed by Kuperberg.Comment: 22 pages, 2 figures; v3: further minor changes, essentially published
versio
SO(10) Cosmic Strings and SU(3) Color Cheshire Charge
Certain cosmic strings that occur in GUT models such as can carry a
magnetic flux which acts nontrivially on objects carrying
quantum numbers. We show that such strings are non-Abelian Alice strings
carrying nonlocalizable colored ``Cheshire" charge. We examine claims made in
the literature that strings can have a long-range, topological
Aharonov-Bohm interaction that turns quarks into leptons, and observe that such
a process is impossible. We also discuss flux-flux scattering using a
multi-sheeted formalism.Comment: 37 Pages, 8 Figures (available upon request) phyzzx, iassns-hep-93-6,
itp-sb-93-6
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