Results 1  10
of
39
Fast Boundary Detection: A Generalization and a New Algorithm”.
 lEEE Trans. Comput.,
, 1977
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Fast Polynomial Factorization Over High Algebraic Extensions of Finite Fields
 In Kuchlin [1997
, 1997
"... New algorithms are presented for factoring polynomials of degree n over the finite field of q elements, where q is a power of a fixed prime number. When log q = n 1+a , where a ? 0 is constant, these algorithms are asymptotically faster than previous known algorithms, the fastest of which require ..."
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Cited by 23 (5 self)
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New algorithms are presented for factoring polynomials of degree n over the finite field of q elements, where q is a power of a fixed prime number. When log q = n 1+a , where a ? 0 is constant, these algorithms are asymptotically faster than previous known algorithms, the fastest of which required time \Omega\Gamma n(log q) 2 ), y or \Omega\Gamma n 3+2a ) in this case, which corresponds to the cost of computing x q modulo an n degree polynomial. The new algorithms factor an arbitrary polynomial in time O(n 3+a+o(1) +n 2:69+1:69a ). All measures are in fixed precision operations, that is in bit complexity. Moreover, in the special case where all the irreducible factors have the same degree, the new algorithms run in time O(n 2:69+1:69a ). In particular, one may test a polynomial for irreducibility in O(n 2:69+1:69a ) bit operations. These results generalize to the case where q = p k , where p is a small prime number relative to q. 1 Introduction The expected run...
MultiWay Partitioning Via Geometric Embeddings, Orderings, and Dynamic Programming
 Orderings, and Dynamic Programming’, in IEEE Trans. on CAD
, 1995
"... This paper presents effective algorithms for multiway partitioning. Confirming ideas originally due to Hall [27], we demonstrate that geometric embeddings of the circuit netlist can lead to highquality kway partitionings. The netlist embeddings are derived via the computation of d eigenvectors o ..."
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Cited by 21 (1 self)
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This paper presents effective algorithms for multiway partitioning. Confirming ideas originally due to Hall [27], we demonstrate that geometric embeddings of the circuit netlist can lead to highquality kway partitionings. The netlist embeddings are derived via the computation of d eigenvectors of the Laplacian for a graph representation of the netlist. As [27] did not specify how to partition such geometric embeddings, we explore various geometric partitioning objectives and algorithms, and find that they are limited because they do not integrate topological information from the netlist. Thus, we also present a new partitioning algorithm that exploits both the geometric embedding and netlist information, as well as a Restricted Partitioning formulation that requires each cluster of the kway partitioning to be contiguous in a given linear ordering. We begin with a ddimensional spectral embedding and construct a heuristic 1dimensional ordering of the modules (combining spacefillin...
The Chiral Phase Transition in QCD: Critical Phenomena and Long Wavelength Pion Oscillations”, appeared
 in QuarkGluon Plasma 2, edited by R. Hwa, World Scientific, 1995; and Krishna Rajagopal in hepph/9703258
"... In QCD with two flavours of massless quarks, the chiral phase transition is plausibly in the same universality class as the classical four component Heisenberg magnet. Therefore, renormalization group techniques developed in the study of phase transitions can be applied to calculate the critical exp ..."
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Cited by 9 (0 self)
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In QCD with two flavours of massless quarks, the chiral phase transition is plausibly in the same universality class as the classical four component Heisenberg magnet. Therefore, renormalization group techniques developed in the study of phase transitions can be applied to calculate the critical exponents which characterize the scaling behaviour of universal quantities near the critical point. As a consequence of this observation, a quantitative description of the universal physics of the chiral phase transition in circumstances where the plasma is close to thermal equilibrium as it passes through the critical temperature can be obtained. This approach to the QCD phase transition has implications both for lattice gauge theory and for heavy ion collisions. Future lattice simulations with longer correlation lengths will provide quantitative measurements of the various exponents and the equation of state for the order parameter as a function of temperature and quark masses. Present lattice simulations already allow many qualitative tests. In a heavy ion collision, the consequence of a long correlation
The edge span of distance two labelings of graphs
 Taiwanese J. Math
, 1997
"... Abstract. The radio channel assignment problem can be cast as a graph coloring problem. Vertices correspond to transmitter locations and their labels (colors) to radio channels. The assignment of frequencies to each transmitter (vertex) must avoid interference which depends on the seperation each pa ..."
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Cited by 7 (2 self)
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Abstract. The radio channel assignment problem can be cast as a graph coloring problem. Vertices correspond to transmitter locations and their labels (colors) to radio channels. The assignment of frequencies to each transmitter (vertex) must avoid interference which depends on the seperation each pair of vertices has. Two levels of interference are assumed in the problem we are concerned. Based on this channel assignment problem, we proposed a graph labelling problem which has two constraints instead of one. We consider the question of finding the minimum edge of this labelling. Several classes of graphs including one that is important to a telecommunication problem have been studied. 1.
Threedimensional unsteady incompressible flow calculations using multigrid
, 1997
"... We apply a robust and computationally efficient multigriddriven algorithm for the simulation of timedependent threedimensional incompressible bluff body wakes at low Reynolds numbers (Re less than or equal to 350). The computational algorithm combines a generalized timeaccurate artificial compre ..."
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Cited by 6 (2 self)
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We apply a robust and computationally efficient multigriddriven algorithm for the simulation of timedependent threedimensional incompressible bluff body wakes at low Reynolds numbers (Re less than or equal to 350). The computational algorithm combines a generalized timeaccurate artificial compressibility approach, a finitevolume discretization in space, and an implicit backward discretization in time. The solution is advanced in time by performing iterative 'pseudotransient ' steadystate calculations at each time step. The key to the algorithm's efficiency is a powerful multigrid scheme that is employed to accelerate the rate of convergence of the pseudotransient iteration. The computational efficiency is improved even further by the application of residual smoothing and local pseudo timestepping techniques, and by using a pointimplicit discretization of the unsteady terms. The solver is implemented on a multiprocessor IBM SP2 computer by using the MPI Standard, and a high parallel scalability is demonstrated. The low Reynolds number regime (Re less than or equal to 500) encompasses flow transitions to unsteadiness and to threedimensionality and attracts considerable attention as an important step on the road to turbulence. In this regime, the slow asymptotics of the wake provide a challenging test for numerical methods since long integration times are necessary to resolve the flow evolution toward a limiting cycle. Our method is extended to three dimensions and applied for low Reynolds number flows over a circular cylinder (Re less than or equal to 250) and a circular semicylinder (Re = 350). The computational results are found to be in close agreement with the available experimental and computational data.
Monomerdimer tatami tilings of rectangular regions
"... In this paper we consider tilings of rectangular regions with two types of tiles, 1 × 2 tiles (dimers) and 1 × 1 tiles (monomers). The tiles must cover the region and satisfy the constraint that no four corners of the tiles meet; such tilings are called tatami tilings. We provide a structural charac ..."
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Cited by 5 (5 self)
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In this paper we consider tilings of rectangular regions with two types of tiles, 1 × 2 tiles (dimers) and 1 × 1 tiles (monomers). The tiles must cover the region and satisfy the constraint that no four corners of the tiles meet; such tilings are called tatami tilings. We provide a structural characterization and use it to prove that the tiling is completely determined by the tiles that are on its border. We prove that the number of tatami tilings of an n × n square with n monomers is n2 n−1. We also show that, for fixedheight, the generating function for the number of tatami tilings of a rectangle is a rational function, and outline an algorithm that produces the generating function.
AUSPICIOUS TATAMI MAT ARRANGEMENTS
"... Abstract. The main purpose of this paper is to introduce the idea of tatami tilings, and to present some of the many interesting and fun questions that arise when studying them. Roughly speaking, we are considering are tilings of rectilinear regions with 1×2 dimer tiles and 1×1 monomer tiles, with t ..."
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Abstract. The main purpose of this paper is to introduce the idea of tatami tilings, and to present some of the many interesting and fun questions that arise when studying them. Roughly speaking, we are considering are tilings of rectilinear regions with 1×2 dimer tiles and 1×1 monomer tiles, with the constraint that no four corners of the tiles meet. Typical problems are to minimize the number of monomers in a tiling, or to count the number of tilings in a particular shape. We determine the underlying structure of tatami tilings of rectangles and use this to prove that the number of tatami tilings of an n × n square with n monomers is n2 n−1. We also prove that, for fixedheight, the number of tatami tilings of a rectangle is a rational function and outline an algorithm that produces the coefficients of the two polynomials of the numerator and the denominator. Many interesting and fun open problems remain to be solved. 1. What is a tatami tiling? Traditionally, a tatami mat is made from a rice straw core, with a covering of woven soft rush straw. Originally intended for nobility in Japan, they are now available in massmarket stores. The typical tatami mat occurs in a 1×2 aspect ratio and various configurations of them are used to cover floors in houses and temples. By parity considerations it may be necessary to introduce mats with a
Intrinsic metrics on graphs – a survey
 Mathematical Technology of Networks (Proc. Bielefeld 2013), volume ??? of Proc. Math. & Stat., page
, 2014
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