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1.
Maximum-weight stable sets and safe lower bounds for graph coloring   总被引:2,自引:0,他引:2  
The best method known for determining lower bounds on the vertex coloring number of a graph is the linear-programming column-generation technique, where variables correspond to stable sets, first employed by Mehrotra and Trick in 1996. We present an implementation of the method that provides numerically-safe results, independent of the floating-point accuracy of linear-programming software. Our work includes an improved branch-and-bound algorithm for maximum-weight stable sets and a parallel branch-and-price framework for graph coloring. Computational results are presented on a collection of standard test instances, including the unsolved challenge problems created by David S. Johnson in 1989.  相似文献
2.

The inversive congruential method is an attractive alternative to the classical linear congruential method for pseudorandom number generation. In this paper we present the first nontrivial bounds on the discrepancy of individual sequences of inversive congruential pseudorandom numbers in parts of the period. The proof is based on a new bound for certain incomplete exponential sums.

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3.
Let q*(G) denote the minimum integer t for which E(G) can be partitioned into t induced matchings of G. Faudree et al. conjectured that q*(G)d2, if G is a bipartite graph and d is the maximum degree of G. In this note, we give an affirmative answer for d=3, the first nontrivial case of this conjecture.  相似文献
4.
Recently, Coppersmith and Shparlinski proved several results on the interpolation of the discrete logarithm in the finite prime field by polynomials modulo p and modulo p-1, respectively. In this paper most of these results are extended to arbitrary .  相似文献
5.
We describe a new dual algorithm for the minimum cost flow problem. It can be regarded as a variation of the best known strongly polynomial minimum cost flow algorithm, due to Orlin. Indeed we obtain the same running time of O(m log m(m+n log n)), where n and m denote the number of vertices and the number of edges. However, in contrast to Orlin's algorithm we work directly with the capacitated network (rather than transforming it to a transshipment problem). Thus our algorithm is applicable to more general problems (like submodular flow) and is likely to be more efficient in practice.  Our algorithm can be interpreted as a cut cancelling algorithm, improving the best known strongly polynomial bound for this important class of algorithms by a factor of m. On the other hand, our algorithm can be considered as a variant of the dual network simplex algorithm. Although dual network simplex algorithms are reportedly quite efficient in practice, the best worst-case running time known so far exceeds the running time of our algorithm by a factor of n.  相似文献
6.
Inversive methods are attractive alternatives to the linear method for pseudorandom number generation. A particularly attractive method is the digital explicit inversive method recently introduced by the authors. We establish some new results on the statistical properties of parallel streams of pseudorandom numbers generated by this method. In particular, we extend the results of the first author on the statistical properties of pseudorandom numbers generated by the explicit inversive congruential method introduced by Eichenauer-Herrmann. These results demonstrate that the new method is eminently suitable for the generation of parallel streams of pseudorandom numbers with desirable properties.  相似文献
7.
The uniformity and irregularities of point distributions can be measured by various kinds of geometric objects. In this paper we prove the existence of point sets that have relatively small irregularities with respect to homothetic copies of a fixed convex body. The results give higher dimensional alternatives to a theorem of Beck.Supported by the Alexander von Humboldt Foundation.  相似文献
8.
 Given a set of disjoint groups of points in the plane, the rectilinear group Steiner tree problem is the problem of finding a shortest interconnection (under the rectilinear metric) which includes at least one point from each group. This is an important generalization of the well-known rectilinear Steiner tree problem which has direct applications in VLSI design: in the detailed routing phase the logical units typically allow the nets to connect to several electrically equivalent ports. We present a first (tailored) exact algorithm for solving the rectilinear group Steiner tree problem (and related variants of the problem). The algorithm essentially constructs a subgraph of the corresponding Hanan grid on which existing algorithms for solving the Steiner tree problem in graphs are applied. The reductions of the Hanan grid are performed by applying point deletions and by generating full Steiner trees on the remaining points. Experimental results for real-world VLSI instances with up to 100 groups are presented. Received: November 7, 2000 / Accepted: December 19, 2001 Published online: September 5, 2002  相似文献
9.
In an article of A. B. Owen (1998, J. Complexity14, 466–489) the question about the distribution properties of digital (tms)-nets in small intervals was raised. We give upper and lower bounds for the maximum number of points of a (tms)-net in these intervals and also provide a way of improving the distribution properties in some cases.  相似文献
10.
In quasi-Monte Carlo methods, point sets of low discrepancy are crucial for accurate results. A class of point sets with low theoretic upper bounds of discrepancy are the digital point sets known as digital (tms)-nets which can be implemented very efficiently. The parameter t is indicative of the quality; i.e., small values of t lead to small upper bounds of the discrepancy. We introduce an effective way to establish this quality parameter t for digital nets constructed over arbitrary finite fields and give an application to the construction of digital nets of high quality.  相似文献
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