28,734 research outputs found
Efficient computation of hashes
The sequential computation of hashes at the core of many distributed storage systems and found, for example, in grid services can hinder efficiency in service quality and even pose security challenges that can only be addressed by the use of parallel hash tree modes. The main contributions of this paper are, first, the identification of several efficiency and security challenges posed by the use of sequential hash computation based on the Merkle-Damgard engine. In addition, alternatives for the parallel computation of hash trees are discussed, and a prototype for a new parallel implementation of the Keccak function, the SHA-3 winner, is introduced
Efficient Computation of Sequence Mappability
Sequence mappability is an important task in genome re-sequencing. In the
-mappability problem, for a given sequence of length , our goal
is to compute a table whose th entry is the number of indices such
that length- substrings of starting at positions and have at
most mismatches. Previous works on this problem focused on heuristic
approaches to compute a rough approximation of the result or on the case of
. We present several efficient algorithms for the general case of the
problem. Our main result is an algorithm that works in time and space for
. It requires a carefu l adaptation of the technique of Cole
et al.~[STOC 2004] to avoid multiple counting of pairs of substrings. We also
show -time algorithms to compute all results for a fixed
and all or a fixed and all . Finally we show
that the -mappability problem cannot be solved in strongly subquadratic
time for unless the Strong Exponential Time Hypothesis
fails.Comment: Accepted to SPIRE 201
Efficient computation of middle levels Gray codes
For any integer a middle levels Gray code is a cyclic listing of
all bitstrings of length that have either or entries equal to
1 such that any two consecutive bitstrings in the list differ in exactly one
bit. The question whether such a Gray code exists for every has been
the subject of intensive research during the last 30 years, and has been
answered affirmatively only recently [T. M\"utze. Proof of the middle levels
conjecture. Proc. London Math. Soc., 112(4):677--713, 2016]. In this work we
provide the first efficient algorithm to compute a middle levels Gray code. For
a given bitstring, our algorithm computes the next bitstrings in the
Gray code in time , which is
on average per bitstring provided that
Efficient Computation of the Characteristic Polynomial
This article deals with the computation of the characteristic polynomial of
dense matrices over small finite fields and over the integers. We first present
two algorithms for the finite fields: one is based on Krylov iterates and
Gaussian elimination. We compare it to an improvement of the second algorithm
of Keller-Gehrig. Then we show that a generalization of Keller-Gehrig's third
algorithm could improve both complexity and computational time. We use these
results as a basis for the computation of the characteristic polynomial of
integer matrices. We first use early termination and Chinese remaindering for
dense matrices. Then a probabilistic approach, based on integer minimal
polynomial and Hensel factorization, is particularly well suited to sparse
and/or structured matrices
Efficient Computation of the Kauffman Bracket
This paper bounds the computational cost of computing the Kauffman bracket of
a link in terms of the crossing number of that link. Specifically, it is shown
that the image of a tangle with boundary points and crossings in the
Kauffman bracket skein module is a linear combination of basis
elements, with each coefficient a polynomial with at most nonzero terms,
each with integer coefficients, and that the link can be built one crossing at
a time as a sequence of tangles with maximum number of boundary points bounded
by for some From this it follows that the computation of the
Kauffman bracket of the link takes time and memory a polynomial in times
$2^{C\sqrt{n}}.
Fuel Efficient Computation in Passive Self-Assembly
In this paper we show that passive self-assembly in the context of the tile
self-assembly model is capable of performing fuel efficient, universal
computation. The tile self-assembly model is a premiere model of self-assembly
in which particles are modeled by four-sided squares with glue types assigned
to each tile edge. The assembly process is driven by positive and negative
force interactions between glue types, allowing for tile assemblies floating in
the plane to combine and break apart over time. We refer to this type of
assembly model as passive in that the constituent parts remain unchanged
throughout the assembly process regardless of their interactions. A
computationally universal system is said to be fuel efficient if the number of
tiles used up per computation step is bounded by a constant. Work within this
model has shown how fuel guzzling tile systems can perform universal
computation with only positive strength glue interactions. Recent work has
introduced space-efficient, fuel-guzzling universal computation with the
addition of negative glue interactions and the use of a powerful non-diagonal
class of glue interactions. Other recent work has shown how to achieve fuel
efficient computation within active tile self-assembly. In this paper we
utilize negative interactions in the tile self-assembly model to achieve the
first computationally universal passive tile self-assembly system that is both
space and fuel-efficient. In addition, we achieve this result using a limited
diagonal class of glue interactions
- …