28 research outputs found
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.
Dagstuhl Reports : Volume 1, Issue 2, February 2011
Online Privacy: Towards Informational Self-Determination on the Internet (Dagstuhl Perspectives Workshop 11061) : Simone Fischer-Hübner, Chris Hoofnagle, Kai Rannenberg, Michael Waidner, Ioannis Krontiris and Michael Marhöfer Self-Repairing Programs (Dagstuhl Seminar 11062) : Mauro Pezzé, Martin C. Rinard, Westley Weimer and Andreas Zeller Theory and Applications of Graph Searching Problems (Dagstuhl Seminar 11071) : Fedor V. Fomin, Pierre Fraigniaud, Stephan Kreutzer and Dimitrios M. Thilikos Combinatorial and Algorithmic Aspects of Sequence Processing (Dagstuhl Seminar 11081) : Maxime Crochemore, Lila Kari, Mehryar Mohri and Dirk Nowotka Packing and Scheduling Algorithms for Information and Communication Services (Dagstuhl Seminar 11091) Klaus Jansen, Claire Mathieu, Hadas Shachnai and Neal E. Youn
Full-fledged Real-Time Indexing for Constant Size Alphabets
In this paper we describe a data structure that supports pattern matching
queries on a dynamically arriving text over an alphabet ofconstant size. Each
new symbol can be prepended to in O(1) worst-case time. At any moment, we
can report all occurrences of a pattern in the current text in
time, where is the length of and is the number of occurrences.
This resolves, under assumption of constant-size alphabet, a long-standing open
problem of existence of a real-time indexing method for string matching (see
\cite{AmirN08})
Sublinear Space Algorithms for the Longest Common Substring Problem
Given documents of total length , we consider the problem of finding a
longest string common to at least of the documents. This problem is
known as the \emph{longest common substring (LCS) problem} and has a classic
space and time solution (Weiner [FOCS'73], Hui [CPM'92]).
However, the use of linear space is impractical in many applications. In this
paper we show that for any trade-off parameter , the LCS
problem can be solved in space and time, thus providing
the first smooth deterministic time-space trade-off from constant to linear
space. The result uses a new and very simple algorithm, which computes a
-additive approximation to the LCS in time and
space. We also show a time-space trade-off lower bound for deterministic
branching programs, which implies that any deterministic RAM algorithm solving
the LCS problem on documents from a sufficiently large alphabet in
space must use
time.Comment: Accepted to 22nd European Symposium on Algorithm
Longest Common Extensions in Sublinear Space
The longest common extension problem (LCE problem) is to construct a data
structure for an input string of length that supports LCE
queries. Such a query returns the length of the longest common prefix of the
suffixes starting at positions and in . This classic problem has a
well-known solution that uses space and query time. In this paper
we show that for any trade-off parameter , the problem can
be solved in space and query time. This
significantly improves the previously best known time-space trade-offs, and
almost matches the best known time-space product lower bound.Comment: An extended abstract of this paper has been accepted to CPM 201
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
Online Detection of Repetitions with Backtracking
In this paper we present two algorithms for the following problem: given a
string and a rational , detect in the online fashion the earliest
occurrence of a repetition of exponent in the string.
1. The first algorithm supports the backtrack operation removing the last
letter of the input string. This solution runs in time and
space, where is the maximal length of a string generated during the
execution of a given sequence of read and backtrack operations.
2. The second algorithm works in time and space,
where is the length of the input string and is the number of
distinct letters. This algorithm is relatively simple and requires much less
memory than the previously known solution with the same working time and space.
a string generated during the execution of a given sequence of read and
backtrack operations.Comment: 12 pages, 5 figures, accepted to CPM 201
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Podeu consultar la versió en castellà a: http://hdl.handle.net/11703/10236