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The error linear complexity spectrum of a periodic sequence is defined to be the ordered list of $$k$$ k -error linear complexities of the sequence. In this paper, we present an algorithm which computes the error linear complexity spectrum for binary sequences with period $$p^{n}$$ p n , where $$p$$ p is an odd prime and $$2$$ 2 is a primitive root modulo $$p^{2}$$ p 2 . [ABSTRACT FROM AUTHOR]

The concept of rainbow connection was introduced by Chartrand et al. [] in 2008. It is interesting and recently quite a lot papers have been published about it. In this survey we attempt to bring together most of the results and papers that dealt with it. We begin with an introduction, and then try to organize the work into five categories, including (strong) rainbow connection number, rainbow k-connectivity, k-rainbow index, rainbow vertex-connection number, algorithms and computational complexity. This survey also contains some conjectures, open problems and questions. [ABSTRACT FROM AUTHOR]

As database technology is applied to more and more application domains, user queries are becoming increasingly complex (e.g. involving a large number of joins and a complex query structure). Query optimizers in existing database management systems (DBMS) were not developed for efficiently processing such queries and often suffer from problems such as intolerably long optimization time and poor optimization results. To tackle this challenge, we present a new similarity-based approach to optimizing complex queries in this paper. The key idea is to identify similar subqueries that often appear in a complex query and share the optimization result among similar subqueries in the query. Different levels of similarity for subqueries are introduced. Efficient algorithms to identify similar queries in a given query and optimize the query based on similarity are presented. Related issues, such as choosing good starting nodes in a query graph, evaluating identified similar subqueries and analyzing algorithm complexities, are discussed. Our experimental results demonstrate that the proposed similarity-based approach is quite promising in optimizing complex queries with similar subqueries in a DBMS. [ABSTRACT FROM AUTHOR]

The m-machine no-wait flowshop scheduling problem, with the objective of minimizing total completion time subject to the constraint that makespan has to be less than or equal to a certain value, is addressed in this paper. First, an algorithm is proposed to find an upper bound on the makespan in case the upper bound is not given or unknown. Given the upper bound on makespan, a proposed algorithm ( PAL) with five versions L (1, 5, 10, 15, and 20) and a genetic algorithm ( GA) are utilized for solving the problem. Furthermore, a dominance relation is established for the case of four machines. The five versions of PAL and GA are evaluated on randomly generated problems with different number of jobs and number of machines. Computational experiments show that the errors of PA10, PA15, and PA20 are much smaller than that of GA while the CPU times of PA10, PA15, and PA20 are significantly smaller than that of GA. Therefore, the algorithms PA10, PA15, and PA20 are superior to the GA algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we first optimize the structure of the Wei-Xiao-Chen algorithm for the linear complexity of sequences over GF( q) with period N = 2 p, where p and q are odd primes, and q is a primitive root modulo p. The second, an union cost is proposed, so that an efficient algorithm for computing the k-error linear complexity of a sequence with period 2 p over GF( q) is derived, where p and q are odd primes, and q is a primitive root modulo p. The third, we give a validity of the proposed algorithm, and also prove that there exists an error sequence e, where the Hamming weight of e is not greater than k, such that the linear complexity of ( s + e) reaches the k-error linear complexity c. We also present a numerical example to illustrate the algorithm. Finally, we present the minimum value k for which the k-error linear complexity is strictly less than the linear complexity. [ABSTRACT FROM AUTHOR]

In this paper we describe a singly exponential algorithm for computing the first Betti number of a given semi-algebraic set. Singly exponential algorithms for computing the zeroth Betti number, and the Euler–Poincaré characteristic, were known before. No singly exponential algorithm was known for computing any of the individual Betti numbers other than the zeroth one. As a consequence we also obtain algorithms for computing semi-algebraic descriptions of the semi-algebraically connected components of any given real algebraic or semi-algebraic set in singly exponential time, which improves on the complexity of the previously published algorithms for this problem. [ABSTRACT FROM AUTHOR]

An algorithm for finding all shortest paths in an undirected network is considered. The following two criteria are used: the minimum number of arcs in a path and a minimum path length. The algorithm is analyzed for complexity, and it is empirically shown that, with increasing the network density, its computational efficiency becomes higher than that of the Floyd algorithm adequately modified to find the shortest path with the use of a two-step criterion. [ABSTRACT FROM AUTHOR]

For binary sequences with period $$p^{n}$$ , where $$p$$ is an odd prime and 2 is a primitive root modulo $$p^{2}$$ , we present an algorithm which computes the minimum number $$k$$ so that the $$k$$ -error linear complexity is not greater than a given constant $$c$$ . An associated error sequence which gives the $$k$$ -error linear complexity is also obtained. [ABSTRACT FROM AUTHOR]

Various methods have been suggested in the past to determine the minimum zone straightness error, but suffer from various drawbacks. A new, fast and simple algorithm is proposed to calculate the straightness error from planar coordinate data. It guarantees the minimum zone solution. An example and test data are provided. Results of simulation experiments to establish the time computational complexity of the algorithm are also presented. [ABSTRACT FROM AUTHOR]