Author

# Paul Pritchard

Other affiliations: University of Queensland, Cornell University

Bio: Paul Pritchard is an academic researcher from Griffith University. The author has contributed to research in topics: Prime number & Association rule learning. The author has an hindex of 11, co-authored 19 publications receiving 306 citations. Previous affiliations of Paul Pritchard include University of Queensland & Cornell University.

##### Papers

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TL;DR: A new algorithm is presented for the problem of finding all primes between 2 and N that improves on Mairson's sieve algorithm by using a dynamic sieve technique that avoids most of the nonprimes in the range 2 to N, and byUsing a tabulation method to simulate multiplications.

Abstract: A new algorithm is presented for the problem of finding all primes between 2 and N. It is based on Mairson's sieve algorithm which uses θ(N) additions and multiplications. The new algorithm improves on this algorithm by using a dynamic sieve technique that avoids most of the nonprimes in the range 2 to N, and by using a tabulation method to simulate multiplications. It is shown to require θ(N/log log N) additions. A related algorithm is outlined that has the same complexity but a storage requirement of only θ(N/log log N) bits.

56 citations

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TL;DR: A simple mathematical framework is developed, which leads to a smoother and more insightful derivation of the new algorithm, and which may be of independent interest to the number theorist.

Abstract: In a previous paper, an algorithm was presented for the classical problem of finding all prime numbers up to a given limit The algorithm was derived therein by transforming a prior algorithm in accordance with some essentially ad hoc observations on the problem
The present paper complements the former by developing a simple mathematical framework, which leads to a smoother and more insightful derivation of the new algorithm, and which may be of independent interest to the number theorist

42 citations

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TL;DR: It is shown that all these algorithms for enumerating the prime numbers up to some limit N emerge from the common idea of a sieve by the judicious use of three simple principles.

Abstract: In recent years several new algorithms have appeared for the problem of enumerating the prime numbers up to some limit N. We show that all these algorithms emerge from the common idea of a sieve by the judicious use of three simple principles.

38 citations

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TL;DR: A parameterized family of algorithms is presented for the problem of finding all prime numbers up to a limit N, and a particular choice of parameters leads to an algorithm that requires only Θ(N) additions and that runs in o( N ) bits.

Abstract: A parameterized family of algorithms is presented for the problem of finding all prime numbers up to a limit N. Many previous algorithms for this problem are shown to correspond to members of this family. A particular choice of parameters leads to an algorithm that requires only Θ(N) additions and that runs in o( N ) bits. The small storage requirement is made possible by a provably compact method of storing all the primes up to some limit.

28 citations

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TL;DR: A matching upper bound on the number of edges in a subset graph is established, and a finer analysis of the algorithm is presented, which confirms the claimed upper bound and shows it to be tight.

Abstract: Let a given collection of sets have size N measured by the sum of the cardinalities. Yellin and Jutla presented an algorithm which constructed the partial order induced by the subset relation (a “subset graph”) in a claimed O ( N 2 /log N ) operations over a dictionary ADT, and exhibited a collection whose subset graph had Θ( N 2 /log 2 N ) edges. This paper first establishes a matching upper bound on the number of edges in a subset graph. It also presents a finer analysis of the algorithm, which confirms the claimed upper bound and shows it to be tight. A simple implementation requiring O (1) bit-parallel operations per ADT operation is presented, along with a variant of the algorithm with an implementation requiring O ( N 2 /log N ) RAM operations.

27 citations

##### Cited by

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TL;DR: This paper presents a polynomial-time algorithm to solve the following problem: given a non-zeroPolynomial fe Q(X) in one variable with rational coefficients, find the decomposition of f into irreducible factors in Q (X).

Abstract: In this paper we present a polynomial-time algorithm to solve the following problem: given a non-zero polynomial fe Q(X) in one variable with rational coefficients, find the decomposition of f into irreducible factors in Q(X). It is well known that this is equivalent to factoring primitive polynomials feZ(X) into irreducible factors in Z(X). Here we call f~ Z(X) primitive if the greatest common divisor of its coefficients (the content of f) is 1. Our algorithm performs well in practice, cf. (8). Its running time, measured in bit operations, is O(nl2+n9(log(fD3).

3,513 citations

01 Jan 1982

TL;DR: In this paper, a polynomial-time algorithm was proposed to decompose a primitive polynomials into irreducible factors in Z(X) if the greatest common divisor of its coefficients is 1.

Abstract: In this paper we present a polynomial-time algorithm to solve the following problem: given a non-zero polynomial fe Q(X) in one variable with rational coefficients, find the decomposition of f into irreducible factors in Q(X). It is well known that this is equivalent to factoring primitive polynomials feZ(X) into irreducible factors in Z(X). Here we call f~ Z(X) primitive if the greatest common divisor of its coefficients (the content of f) is 1. Our algorithm performs well in practice, cf. (8). Its running time, measured in bit operations, is O(nl2+n9(log(fD3).

3,248 citations

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TL;DR: A method of user password authentication is described which is secure even if an intruder can read the system's data, and can tamper with or eavesdrop on the communication between the user and the system.

Abstract: A method of user password authentication is described which is secure even if an intruder can read the system's data, and can tamper with or eavesdrop on the communication between the user and the system. The method assumes a secure one-way encryption function and can be implemented with a microcomputer in the user's terminal.

2,874 citations

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01 Jan 2000

TL;DR: This thesis examines how discernibility-based methods can be equipped to posses several qualities that are needed for analyzing tabular medical data, and how these models can be evaluated according to these qualities.

Abstract: This thesis examines how discernibility-based methods can be equipped to posses several qualities that are needed for analyzing tabular medical data, and how these models can be evaluated according ...

281 citations

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TL;DR: Whether the sentiment analysis tools agree with the sentiment recognized by human evaluators (as reported in an earlier study) as well as with each other is studied.

Abstract: Recent years have seen an increasing attention to social aspects of software engineering, including studies of emotions and sentiments experienced and expressed by the software developers. Most of these studies reuse existing sentiment analysis tools such as SentiStrength and NLTK. However, these tools have been trained on product reviews and movie reviews and, therefore, their results might not be applicable in the software engineering domain. In this paper we study whether the sentiment analysis tools agree with the sentiment recognized by human evaluators (as reported in an earlier study) as well as with each other. Furthermore, we evaluate the impact of the choice of a sentiment analysis tool on software engineering studies by conducting a simple study of differences in issue resolution times for positive, negative and neutral texts. We repeat the study for seven datasets (issue trackers and Stack Overflow questions) and different sentiment analysis tools and observe that the disagreement between the tools can lead to diverging conclusions. Finally, we perform two replications of previously published studies and observe that the results of those studies cannot be confirmed when a different sentiment analysis tool is used.

166 citations