2,832 research outputs found
Fingerprint databases for theorems
We discuss the advantages of searchable, collaborative, language-independent
databases of mathematical results, indexed by "fingerprints" of small and
canonical data. Our motivating example is Neil Sloane's massively influential
On-Line Encyclopedia of Integer Sequences. We hope to encourage the greater
mathematical community to search for the appropriate fingerprints within each
discipline, and to compile fingerprint databases of results wherever possible.
The benefits of these databases are broad - advancing the state of knowledge,
enhancing experimental mathematics, enabling researchers to discover unexpected
connections between areas, and even improving the refereeing process for
journal publication.Comment: to appear in Notices of the AM
Optimal Substring-Equality Queries with Applications to Sparse Text Indexing
We consider the problem of encoding a string of length from an integer
alphabet of size so that access and substring equality queries (that
is, determining the equality of any two substrings) can be answered
efficiently. Any uniquely-decodable encoding supporting access must take
bits. We describe a new data
structure matching this lower bound when while supporting
both queries in optimal time. Furthermore, we show that the string can
be overwritten in-place with this structure. The redundancy of
bits and the constant query time break exponentially a lower bound that is
known to hold in the read-only model. Using our new string representation, we
obtain the first in-place subquadratic (indeed, even sublinear in some cases)
algorithms for several string-processing problems in the restore model: the
input string is rewritable and must be restored before the computation
terminates. In particular, we describe the first in-place subquadratic Monte
Carlo solutions to the sparse suffix sorting, sparse LCP array construction,
and suffix selection problems. With the sole exception of suffix selection, our
algorithms are also the first running in sublinear time for small enough sets
of input suffixes. Combining these solutions, we obtain the first
sublinear-time Monte Carlo algorithm for building the sparse suffix tree in
compact space. We also show how to derandomize our algorithms using small
space. This leads to the first Las Vegas in-place algorithm computing the full
LCP array in time and to the first Las Vegas in-place algorithms
solving the sparse suffix sorting and sparse LCP array construction problems in
time. Running times of these Las Vegas
algorithms hold in the worst case with high probability.Comment: Refactored according to TALG's reviews. New w.h.p. bounds and Las
Vegas algorithm
Existentially Restricted Quantified Constraint Satisfaction
The quantified constraint satisfaction problem (QCSP) is a powerful framework
for modelling computational problems. The general intractability of the QCSP
has motivated the pursuit of restricted cases that avoid its maximal
complexity. In this paper, we introduce and study a new model for investigating
QCSP complexity in which the types of constraints given by the existentially
quantified variables, is restricted. Our primary technical contribution is the
development and application of a general technology for proving positive
results on parameterizations of the model, of inclusion in the complexity class
coNP
A new problem in string searching
We describe a substring search problem that arises in group presentation
simplification processes. We suggest a two-level searching model: skip and
match levels. We give two timestamp algorithms which skip searching parts of
the text where there are no matches at all and prove their correctness. At the
match level, we consider Harrison signature, Karp-Rabin fingerprint, Bloom
filter and automata based matching algorithms and present experimental
performance figures.Comment: To appear in Proceedings Fifth Annual International Symposium on
Algorithms and Computation (ISAAC'94), Lecture Notes in Computer Scienc
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