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1. An Efficient Trip Planning Algorithm Under Constraints | |||
Jinling Bao,Xiaochun Yang,Bin Wang | |||
Computer Science and Technology 08 August 2013 | |||
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Abstract:The problem of trip planning has received wide concerns in recent years. More and more people require the service of automatically confirming the optimal tour route. When users assign the source and the destination, and the time limit of the tour, how can automatically decide the optimal tour route with the highest sum of the popularity scores of scenic spots. Current methods for trip planning are on the setting that providing with the route which is composed of the scenic spots to travel. These would work poorly for the pre-mentioned problem when the route satisfying the constraints can not be found. Thus we adjust the setting to giving the route composed of the scenic spots which users visit or simply pass by. Obviously, the modified problem would incur larger search cost as each scenic spot in the given route has two states. It can be demonstrated that this new problem is NP hard, making it difficult to find an efficient exact algorithm for the present. In this paper, we propose a greedy strategy based algorithm to solve the trip planning problem, and we also present an improved algorithm with better performance. The experimental results on synthesized and real data sets reveal that our algorithm is able to find the approximately optimal path in high efficiency. | |||
TO cite this article:Jinling Bao,Xiaochun Yang,Bin Wang. An Efficient Trip Planning Algorithm Under Constraints[OL].[ 8 August 2013] http://en.paper.edu.cn/en_releasepaper/content/4554413 |
2. A complete algorithm to find exact minimal polynomial by approximations | |||
Xiaolin Qin,Yong Feng,Jingwei Chen,Jingzhong Zhang | |||
Computer Science and Technology 11 January 2010 | |||
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Abstract:We present a complete algorithm for finding an exact minimal polynomial from its approximate value by using an improved parameterized integer relation construction method. Our result is superior to the existence of error controlling on obtaining an exact rational number from its approximation. The algorithm is applicable for finding exact minimal polynomial of an algebraic number by its approximate root. This also enables us to provide an efficient method of converting the rational approximation representation to the minimal polynomial representation, and devise a simple algorithm to factor multivariate polynomials with rational coefficients. Compared with the subsistent methods, our method combines advantage of high efficiency in numerical computation, and exact, stable results in symbolic computation. we also discuss some applications to some transcendental numbers by approximations. Moreover, the \\emph{Digits} of our algorithm is far less than the LLL-lattice basis reduction technique in theory. In this paper, we completely implement how to obtain exact results by numerical approximate computations. | |||
TO cite this article:Xiaolin Qin,Yong Feng,Jingwei Chen, et al. A complete algorithm to find exact minimal polynomial by approximations[OL].[11 January 2010] http://en.paper.edu.cn/en_releasepaper/content/38727 |
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