426 research outputs found
On the String Consensus Problem and the Manhattan Sequence Consensus Problem
In the Manhattan Sequence Consensus problem (MSC problem) we are given
integer sequences, each of length , and we are to find an integer sequence
of length (called a consensus sequence), such that the maximum
Manhattan distance of from each of the input sequences is minimized. For
binary sequences Manhattan distance coincides with Hamming distance, hence in
this case the string consensus problem (also called string center problem or
closest string problem) is a special case of MSC. Our main result is a
practically efficient -time algorithm solving MSC for sequences.
Practicality of our algorithms has been verified experimentally. It improves
upon the quadratic algorithm by Amir et al.\ (SPIRE 2012) for string consensus
problem for binary strings. Similarly as in Amir's algorithm we use a
column-based framework. We replace the implied general integer linear
programming by its easy special cases, due to combinatorial properties of the
MSC for . We also show that for a general parameter any instance
can be reduced in linear time to a kernel of size , so the problem is
fixed-parameter tractable. Nevertheless, for this is still too large
for any naive solution to be feasible in practice.Comment: accepted to SPIRE 201
Gradual sub-lattice reduction and a new complexity for factoring polynomials
We present a lattice algorithm specifically designed for some classical
applications of lattice reduction. The applications are for lattice bases with
a generalized knapsack-type structure, where the target vectors are boundably
short. For such applications, the complexity of the algorithm improves
traditional lattice reduction by replacing some dependence on the bit-length of
the input vectors by some dependence on the bound for the output vectors. If
the bit-length of the target vectors is unrelated to the bit-length of the
input, then our algorithm is only linear in the bit-length of the input
entries, which is an improvement over the quadratic complexity floating-point
LLL algorithms. To illustrate the usefulness of this algorithm we show that a
direct application to factoring univariate polynomials over the integers leads
to the first complexity bound improvement since 1984. A second application is
algebraic number reconstruction, where a new complexity bound is obtained as
well
Revised Program. New England Intercollegiate Geological Excursion: Montreal, 1931
Program includes visits to St. Helen Island, Mount Royal, Pre-Cambrian of the Laurentians, and the Appalachia front in the vicinity of Phillipsburg, Que
Landau-Ginzburg Description of Boundary Critical Phenomena in Two Dimensions
The Virasoro minimal models with boundary are described in the
Landau-Ginzburg theory by introducing a boundary potential, function of the
boundary field value. The ground state field configurations become non-trivial
and are found to obey the soliton equations. The conformal invariant boundary
conditions are characterized by the reparametrization-invariant data of the
boundary potential, that are the number and degeneracies of the stationary
points. The boundary renormalization group flows are obtained by varying the
boundary potential while keeping the bulk critical: they satisfy new selection
rules and correspond to real deformations of the Arnold simple singularities of
A_k type. The description of conformal boundary conditions in terms of boundary
potential and associated ground state solitons is extended to the N=2
supersymmetric case, finding agreement with the analysis of A-type boundaries
by Hori, Iqbal and Vafa.Comment: 42 pages, 13 figure
High-Performance Computer Algebra: A Hecke Algebra Case Study
We describe the first ever parallelisation of an algebraic computation at modern HPC scale. Our case study poses challenges typical of the domain: it is a multi-phase application with dynamic task creation and irregular parallelism over complex control and data structures.
Our starting point is a sequential algorithm for finding invariant bilinear forms in the representation theory of Hecke algebras, implemented in the GAP computational group theory system. After optimising the sequential code we develop a parallel algorithm that exploits the new skeleton-based SGP2 framework to parallelise the three most computationally-intensive phases. To this end we develop a new domain-specific skeleton, parBufferTryReduce. We report good parallel performance both on a commodity cluster and on a national HPC, delivering speedups up to 548 over the optimised sequential implementation on 1024 cores
Granular Solid Hydrodynamics
Granular elasticity, an elasticity theory useful for calculating static
stress distribution in granular media, is generalized to the dynamic case by
including the plastic contribution of the strain. A complete hydrodynamic
theory is derived based on the hypothesis that granular medium turns
transiently elastic when deformed. This theory includes both the true and the
granular temperatures, and employs a free energy expression that encapsulates a
full jamming phase diagram, in the space spanned by pressure, shear stress,
density and granular temperature. For the special case of stationary granular
temperatures, the derived hydrodynamic theory reduces to {\em hypoplasticity},
a state-of-the-art engineering model.Comment: 42 pages 3 fi
A Loop-Aware Search Strategy for Automated Performance Analysis
Automated online search is a powerful technique for performance diagnosis. Such a search can change the types of experiments it performs while the program is running, making decisions based on live performance data. Previous research has addressed search speed and scaling searches to large codes and many nodes. This paper explores using a finer granularity for the bottlenecks that we locate in an automated online search, i.e., refining the search to bottlenecks localized to loops. The ability to insert and remove instrumentation on-the-fly means an online search can utilize fine-grain program structure in ways that are infeasible using other performance diagnosis techniques. We automatically detect
loops in a program�s binary control flow graph and use this information to efficiently instrument loops. We implemented our new strategy in an existing automated online performance tool, Paradyn. Results for several sequential and parallel applications show that a loop-aware search strategy can increase bottleneck precision without compromising search time or cost
Barrier effects on the collective excitations of split Bose-Einstein condensates
We investigate the collective excitations of a single-species Bose gas at T=0
in a harmonic trap where the confinement undergoes some splitting along one
spatial direction. We mostly consider onedimensional potentials consisting of
two harmonic wells separated a distance 2 z_0, since they essentially contain
all the barrier effects that one may visualize in the 3D situation. We find,
within a hydrodynamic approximation, that regardless the dimensionality of the
system, pairs of levels in the excitation spectrum, corresponding to
neighbouring even and odd excitations, merge together as one increases the
barrier height up to the current value of the chemical potential. The
excitation spectra computed in the hydrodynamical or Thomas-Fermi limit are
compared with the results of exactly solving the time-dependent
Gross-Pitaevskii equation. We analyze as well the characteristics of the
spatial pattern of excitations of threedimensional boson systems according to
the amount of splitting of the condensate.Comment: RevTeX, 12 pages, 13 ps figure
An EPTAS for scheduling jobs on uniform processors using an MILP relaxation with a constant number of integral variables
We present an efficient polynomial time approximation scheme (EPTAS) for scheduling on uniform processors, i.e. finding a minimum length schedule for a set of n independent jobs on m processors with different speeds (a fundamental NP-hard scheduling problem). The previous best polynomial time approximation scheme (PTAS) by Hochbaum and Shmoys has a running time of (n/\epsilon)^{O(1/\epsilon^2)}. Our algorithm, based on a new mixed integer linear programming (MILP) formulation with a constant number of integral variables and an interesting rounding method, finds a schedule whose length is within a relative error of the optimum, and has running time 2^{O(1/\epsilon^2 \log(1/\epsilon)^3)} + poly(n)
Square root algorithms for the number field sieve
The original publication is available at www.springerlink.comInternational audienceWe review several methods for the square root step of the Number Field Sieve, and present an original one, based on the Chinese Remainder Theorem
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