57,372 research outputs found
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
Approximating Approximate Pattern Matching
Given a text of length and a pattern of length , the
approximate pattern matching problem asks for computation of a particular
\emph{distance} function between and every -substring of . We
consider a multiplicative approximation variant of this
problem, for distance function. In this paper, we describe two
-approximate algorithms with a runtime of
for all (constant) non-negative values
of . For constant we show a deterministic
-approximation algorithm. Previously, such run time was known
only for the case of distance, by Gawrychowski and Uzna\'nski [ICALP
2018] and only with a randomized algorithm. For constant we
show a randomized algorithm for the , thereby providing a smooth
tradeoff between algorithms of Kopelowitz and Porat [FOCS~2015, SOSA~2018] for
Hamming distance (case of ) and of Gawrychowski and Uzna\'nski for
distance
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
Specification Patterns for Robotic Missions
Mobile and general-purpose robots increasingly support our everyday life,
requiring dependable robotics control software. Creating such software mainly
amounts to implementing their complex behaviors known as missions. Recognizing
the need, a large number of domain-specific specification languages has been
proposed. These, in addition to traditional logical languages, allow the use of
formally specified missions for synthesis, verification, simulation, or guiding
the implementation. For instance, the logical language LTL is commonly used by
experts to specify missions, as an input for planners, which synthesize the
behavior a robot should have. Unfortunately, domain-specific languages are
usually tied to specific robot models, while logical languages such as LTL are
difficult to use by non-experts. We present a catalog of 22 mission
specification patterns for mobile robots, together with tooling for
instantiating, composing, and compiling the patterns to create mission
specifications. The patterns provide solutions for recurrent specification
problems, each of which detailing the usage intent, known uses, relationships
to other patterns, and---most importantly---a template mission specification in
temporal logic. Our tooling produces specifications expressed in the LTL and
CTL temporal logics to be used by planners, simulators, or model checkers. The
patterns originate from 245 realistic textual mission requirements extracted
from the robotics literature, and they are evaluated upon a total of 441
real-world mission requirements and 1251 mission specifications. Five of these
reflect scenarios we defined with two well-known industrial partners developing
human-size robots. We validated our patterns' correctness with simulators and
two real robots
siEDM: an efficient string index and search algorithm for edit distance with moves
Although several self-indexes for highly repetitive text collections exist,
developing an index and search algorithm with editing operations remains a
challenge. Edit distance with moves (EDM) is a string-to-string distance
measure that includes substring moves in addition to ordinal editing operations
to turn one string into another. Although the problem of computing EDM is
intractable, it has a wide range of potential applications, especially in
approximate string retrieval. Despite the importance of computing EDM, there
has been no efficient method for indexing and searching large text collections
based on the EDM measure. We propose the first algorithm, named string index
for edit distance with moves (siEDM), for indexing and searching strings with
EDM. The siEDM algorithm builds an index structure by leveraging the idea
behind the edit sensitive parsing (ESP), an efficient algorithm enabling
approximately computing EDM with guarantees of upper and lower bounds for the
exact EDM. siEDM efficiently prunes the space for searching query strings by
the proposed method, which enables fast query searches with the same guarantee
as ESP. We experimentally tested the ability of siEDM to index and search
strings on benchmark datasets, and we showed siEDM's efficiency.Comment: 23 page
Asymptotics for minimal overlapping patterns for generalized Euler permutations, standard tableaux of rectangular shape, and column strict arrays
A permutation in the symmetric group is minimally overlapping if
any two consecutive occurrences of in a permutation can share
at most one element. B\'ona \cite{B} showed that the proportion of minimal
overlapping patterns in is at least . Given a permutation ,
we let denote the set of descents of . We study
the class of permutations whose descent set is contained in
the set . For example, up-down permutations in
are the set of permutations whose descent equal such that
. There are natural analogues of
the minimal overlapping permutations for such classes of permutations and we
study the proportion of minimal overlapping patterns for each such class. We
show that the proportion of minimal overlapping permutations in such classes
approaches as goes to infinity. We also study the proportion of minimal
overlapping patterns in standard Young tableaux of shape .Comment: Accepted by Discrete Math and Theoretical Computer Science. Thank
referees' for their suggestion
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