26 research outputs found
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
Fully dynamic data structure for LCE queries in compressed space
A Longest Common Extension (LCE) query on a text of length asks for
the length of the longest common prefix of suffixes starting at given two
positions. We show that the signature encoding of size [Mehlhorn et al., Algorithmica 17(2):183-198,
1997] of , which can be seen as a compressed representation of , has a
capability to support LCE queries in time,
where is the answer to the query, is the size of the Lempel-Ziv77
(LZ77) factorization of , and is an integer that can be handled
in constant time under word RAM model. In compressed space, this is the fastest
deterministic LCE data structure in many cases. Moreover, can be
enhanced to support efficient update operations: After processing
in time, we can insert/delete any (sub)string of length
into/from an arbitrary position of in time, where . This yields
the first fully dynamic LCE data structure. We also present efficient
construction algorithms from various types of inputs: We can construct
in time from uncompressed string ; in
time from grammar-compressed string
represented by a straight-line program of size ; and in time from LZ77-compressed string with factors. On top
of the above contributions, we show several applications of our data structures
which improve previous best known results on grammar-compressed string
processing.Comment: arXiv admin note: text overlap with arXiv:1504.0695
Implementasi Algoritma Boyer Moore Pada Aplikasi Kamus Istilah Kebidanan Berbasis Web
The lack of understanding in obstetrics and limit of instructional media has become one of the factors in the making of dictionary application of midwifery. The current dictionary is still a thick book with many terms in it and difficult to use. dictionary midwifery terms have a weakness in the search process, because users should search for words and terms manually by opening pages per page on the dictionary and existing data could not be changed.Keywords: Algorithm, Boyer Moore, Midwifery Dictionary
Fast equivalence-checking for normed context-free processes
Bisimulation equivalence is decidable in polynomial time over normed graphs generated by a context-free grammar. We present a new algorithm, working in time , thus improving the previously known complexity . It also improves the previously known complexity of the equality problem for simple grammars