66,152 research outputs found
Matching of Compressed Patterns with Character-Variables
We consider the problem of finding an instance of a string-pattern s in a given string under compression by straight line programs (SLP). The variables of the string pattern can be instantiated by single characters. This is a generalisation of the fully compressed pattern match, which is the task of finding a compressed string in another compressed string, which is known to have a polynomial time algorithm.
We mainly investigate patterns s that are linear in the variables, i.e. variables occur at most once in s, also known as partial words.
We show that fully compressed pattern matching with linear patterns can be performed in polynomial time. A polynomial-sized representation of all matches and all substitutions is also computed.
Also, a related algorithm is given that computes all periods of a compressed linear pattern in polynomial time. A technical key result on the structure of partial words shows that an overlap of h+2 copies of a partial word w with at most h holes implies that w is strongly periodic
Dictionary matching in a stream
We consider the problem of dictionary matching in a stream. Given a set of
strings, known as a dictionary, and a stream of characters arriving one at a
time, the task is to report each time some string in our dictionary occurs in
the stream. We present a randomised algorithm which takes O(log log(k + m))
time per arriving character and uses O(k log m) words of space, where k is the
number of strings in the dictionary and m is the length of the longest string
in the dictionary
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
Finding the Leftmost Critical Factorization on Unordered Alphabet
We present a linear time and space algorithm computing the leftmost critical
factorization of a given string on an unordered alphabet.Comment: 13 pages, 13 figures (accepted to Theor. Comp. Sci.
Edit Distance: Sketching, Streaming and Document Exchange
We show that in the document exchange problem, where Alice holds and Bob holds , Alice can send Bob a message of
size bits such that Bob can recover using the
message and his input if the edit distance between and is no more
than , and output "error" otherwise. Both the encoding and decoding can be
done in time . This result significantly
improves the previous communication bounds under polynomial encoding/decoding
time. We also show that in the referee model, where Alice and Bob hold and
respectively, they can compute sketches of and of sizes
bits (the encoding), and send to the referee, who can
then compute the edit distance between and together with all the edit
operations if the edit distance is no more than , and output "error"
otherwise (the decoding). To the best of our knowledge, this is the first
result for sketching edit distance using bits.
Moreover, the encoding phase of our sketching algorithm can be performed by
scanning the input string in one pass. Thus our sketching algorithm also
implies the first streaming algorithm for computing edit distance and all the
edits exactly using bits of space.Comment: Full version of an article to be presented at the 57th Annual IEEE
Symposium on Foundations of Computer Science (FOCS 2016
Real-time motion data annotation via action string
Even though there is an explosive growth of motion capture data, there is still a lack of efficient and reliable methods to automatically annotate all the motions in a database. Moreover, because of the popularity of mocap devices in home entertainment systems, real-time human motion annotation or recognition becomes more and more imperative. This paper presents a new motion annotation method that achieves both the aforementioned two targets at the same time. It uses a probabilistic pose feature based on the Gaussian Mixture Model to represent each pose. After training a clustered pose feature model, a motion clip could be represented as an action string. Then, a dynamic programming-based string matching method is introduced to compare the differences between action strings. Finally, in order to achieve the real-time target, we construct a hierarchical action string structure to quickly label each given action string. The experimental results demonstrate the efficacy and efficiency of our method
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