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55
ARCHITECTUREAWARE CLASSICAL TAYLOR SHIFT BY 1
, 2005
"... We present algorithms that outperform straightforward implementations of classical Taylor shift by 1. For input polynomials of low degrees a method of the SACLIB library is faster than straightforward implementations by a factor of at least 2; for higher degrees we develop a method that is faster th ..."
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Cited by 17 (2 self)
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We present algorithms that outperform straightforward implementations of classical Taylor shift by 1. For input polynomials of low degrees a method of the SACLIB library is faster than straightforward implementations by a factor of at least 2; for higher degrees we develop a method that is faster than straightforward implementations by a factor of up to 7. Our Taylor shift algorithm requires more word additions than straightforward implementations but it reduces the number of cycles per word addition by reducing memory tra c and the number of carry computations. The introduction of signed digits, suspended normalization, radix reduction, and delayed carry propagation enables our algorithm to take advantage of the technique of register tiling which is commonly used by optimizing compilers. While our algorithm is written in a highlevel language, it depends on several parameters that can be tuned to the underlying architecture.
Geometric Pattern Matching: A Performance Study
, 1999
"... In this paper, we undertake a performance study of some recent algorithms for geometric pattern matching. These algorithms cover two general paradigms for pattern matching; alignment and combinatorial pattern matching. We present analytical and empirical evaluations of these schemes. Our results ind ..."
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Cited by 14 (1 self)
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In this paper, we undertake a performance study of some recent algorithms for geometric pattern matching. These algorithms cover two general paradigms for pattern matching; alignment and combinatorial pattern matching. We present analytical and empirical evaluations of these schemes. Our results indicate that a proper implementation of an alignmentbased method outperforms other (often asymptotically better) approaches.
Fast PDA Synchronization Using Characteristic Polynomial Interpolation
 Proc. INFOCOM
, 2002
"... Modern Personal Digital Assistant (PDA) architectures often utilize a wholesale data transfer protocol known as "slow sync" for synchronizing PDAs with Personal Computers (PCs). This approach is markedly inefficient with respect to bandwidth usage and latency, since the PDA and PC typically share ma ..."
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Cited by 12 (8 self)
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Modern Personal Digital Assistant (PDA) architectures often utilize a wholesale data transfer protocol known as "slow sync" for synchronizing PDAs with Personal Computers (PCs). This approach is markedly inefficient with respect to bandwidth usage and latency, since the PDA and PC typically share many common records. We propose, analyze, and implement a novel PDA synchronization scheme (CPIsync) predicated upon recent informationtheoretic research. The salient property of this scheme is that its communication complexity depends on the number of differences between the PDA and PC, and is essentially independent of the overall number of records. Moreover, our implementation shows that the computational complexity of CPIsync is practical, and that the overall latency is typically much smaller than that of slow sync. Thus, CPIsync has potential for significantly improving synchronization protocols for PDAs and, more generally, for heterogeneous networks of many machines.
A Distributed kAnonymity Protocol for Location Privacy,” Centre for Applied Cryptographic Research
, 2008
"... Abstract—To benefit from a locationbased service, a person must reveal her location to the service. However, knowing the person’s location might allow the service to reidentify the person. Location privacy based on kanonymity addresses this threat by cloaking the person’s location such that there ..."
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Cited by 10 (2 self)
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Abstract—To benefit from a locationbased service, a person must reveal her location to the service. However, knowing the person’s location might allow the service to reidentify the person. Location privacy based on kanonymity addresses this threat by cloaking the person’s location such that there are at least k − 1 other people within the cloaked area and by revealing only the cloaked area to a locationbased service. Previous research has explored two ways of cloaking: First, have a central server that knows everybody’s location determine the cloaked area. However, this server needs to be trusted by all users and is a single point of failure. Second, have users jointly determine the cloaked area. However, this approach requires that all users trust each other, which will likely not hold in practice. We propose a distributed approach that does not have these drawbacks. Our approach assumes that there are multiple servers, each deployed by a different organization. A user’s location is known to only one of the servers (e.g., to her cellphone provider), so there is no single entity that knows everybody’s location. With the help of cryptography, the servers and a user jointly determine whether the kanonymity property holds for the user’s area, without the servers learning any additional information, not even whether the property holds. A user learns whether the kanonymity property is satisfied and no other information. The evaluation of our sample implementation shows that our distributed kanonymity protocol is sufficiently fast to be practical. Moreover, our protocol integrates well with existing infrastructures for locationbased services, as opposed to the previous research. I.
Spreading Rumors Cheaply, Quickly, And Reliably
, 2002
"... Gossip protocols have been shown to be a useful tool in the development of simple, robust, and efficient distributed systems. This thesis addresses a number of problems associated with gossip protocols, including dealing with the failure of a large fraction of the hosts in a system, accommodating th ..."
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Cited by 9 (0 self)
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Gossip protocols have been shown to be a useful tool in the development of simple, robust, and efficient distributed systems. This thesis addresses a number of problems associated with gossip protocols, including dealing with the failure of a large fraction of the hosts in a system, accommodating the topology of the underlying network, improving the efficiency of information exchange between hosts, and tolerating Byzantine failures.
HIGHPERFORMANCE IMPLEMENTATIONS OF THE DESCARTES METHOD
, 2006
"... The Descartes method for polynomial real root isolation can be performed with respect to monomial bases and with respect to Bernstein bases. The first variant uses Taylor shift by 1 as its main subalgorithm, the second uses de Casteljau’s algorithm. When applied to integer polynomials, the two vari ..."
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Cited by 9 (0 self)
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The Descartes method for polynomial real root isolation can be performed with respect to monomial bases and with respect to Bernstein bases. The first variant uses Taylor shift by 1 as its main subalgorithm, the second uses de Casteljau’s algorithm. When applied to integer polynomials, the two variants have codominant, almost tight computing time bounds. Implementations of either variant can obtain speedups over previous stateoftheart implementations by more than an order of magnitude if they use features of the processor architecture. We present an implementation of the Bernsteinbases variant of the Descartes method that automatically generates architectureaware highlevel code and leaves further optimizations to the compiler. We compare the performance of our implementation, algorithmically tuned implementations of the monomial and Bernstein variants, and architectureunaware implementations of both variants on four different processor architectures and for three classes of input polynomials.
Fast computation with two algebraic numbers
 September
, 2002
"... We propose fast algorithms for computing composed products and composed sums, as well as diamond products of univariate polynomials. These operations correspond to special resultants, that we compute using power sums of roots of polynomials, by means of their generating series. ..."
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Cited by 8 (3 self)
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We propose fast algorithms for computing composed products and composed sums, as well as diamond products of univariate polynomials. These operations correspond to special resultants, that we compute using power sums of roots of polynomials, by means of their generating series.
Combinatorial and experimental methods for approximate point pattern matching
 Algorithmica
, 2003
"... Point pattern matching is an important problem in computational geometry, with applications in areas like computer vision, object recognition, molecular modelling, and image registration. Traditionally, it has been studied in an exact formulation, where the input point sets are given with arbitrary ..."
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Cited by 6 (0 self)
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Point pattern matching is an important problem in computational geometry, with applications in areas like computer vision, object recognition, molecular modelling, and image registration. Traditionally, it has been studied in an exact formulation, where the input point sets are given with arbitrary precision. This leads to algorithms that typically have running times of the order of high degree polynomials, and require robust calculations of intersection points of high degree surfaces. We study approximate point pattern matching, with the goal of developing algorithms that are more efficient and more practical than exact algorithms. Our work is motivated by the observation that in practice, data sets that form instances of pattern matching problems are noisy, and so approximate formulations are more appropriate. We present new and efficient algorithms for approximate point pattern matching in two and three dimensions, based on approximate combinatorial distance bounds on sets of points, and via the use of methods from combinatorial pattern matching. We also present an average case analysis and a detailed empirical study of our methods.
A Multilevel Blocking Distinctdegree Factorization Algorithm
 CONTEMPORARY MATHEMATICS
, 2008
"... We give a new algorithm for performing the distinctdegree factorization of a polynomial P(x) over GF(2), using a multilevel blocking strategy. The coarsest level of blocking replaces GCD computations by multiplications, as suggested by Pollard (1975), von zur Gathen and Shoup (1992), and others. ..."
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Cited by 5 (4 self)
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We give a new algorithm for performing the distinctdegree factorization of a polynomial P(x) over GF(2), using a multilevel blocking strategy. The coarsest level of blocking replaces GCD computations by multiplications, as suggested by Pollard (1975), von zur Gathen and Shoup (1992), and others. The novelty of our approach is that a finer level of blocking replaces multiplications by squarings, which speeds up the computation in GF(2)[x]/P(x) of certain interval polynomials when P(x) is sparse. As an application we give a fast algorithm to search for all irreducible trinomials x r + x s + 1 of degree r over GF(2), while producing a certificate that can be checked in less time than the full search. Naive algorithms cost O(r 2) per trinomial, thus O(r 3) to search over all trinomials of given degree r. Under a plausible assumption about the distribution of factors of trinomials, the new algorithm has complexity O(r 2 (log r) 3/2 (log log r) 1/2) for the search over all trinomials of degree r. Our implementation achieves a speedup of greater than a factor of 560 over the naive algorithm in the case r = 24036583 (a Mersenne exponent). Using our program, we have found two new primitive trinomials of degree 24036583 over GF(2) (the previous record degree was 6972593).
Faster Multiplication in GF(2)[x]
"... Abstract. In this paper, we discuss an implementation of various algorithms for multiplying polynomials in GF(2)[x]: variants of the window methods, Karatsuba’s, ToomCook’s, Schönhage’s and Cantor’s algorithms. For most of them, we propose improvements that lead to practical speedups. ..."
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Cited by 5 (2 self)
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Abstract. In this paper, we discuss an implementation of various algorithms for multiplying polynomials in GF(2)[x]: variants of the window methods, Karatsuba’s, ToomCook’s, Schönhage’s and Cantor’s algorithms. For most of them, we propose improvements that lead to practical speedups.