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71.
Mihai Ciucu 《Discrete Mathematics》2007,307(15):1957-1960
The even Aztec diamond ADn is known to have precisely four times more spanning trees than the odd Aztec diamond ODn—this was conjectured by Stanley and first proved by Knuth. We present a short combinatorial proof of this fact in the case of odd n. Our proof works also for the more general case of odd-by-odd Aztec rectangles. 相似文献
72.
Enrico Casadio Tarabusi Alessandro Figà -Talamanca 《Proceedings of the American Mathematical Society》2007,135(7):2165-2175
We determine the spectrum and the resolvent operator of a drifted Laplace operator on a homogeneous tree, obtaining qualitatively different results according to the sign of the drift in the direction of a boundary point.
73.
Jan-Arild Audestad Alexei A. Gaivoronski Adrian Werner 《Annals of Operations Research》2006,142(1):19-39
In a previous paper, Gouveia and Magnanti (2003) found diameter-constrained minimal spanning and Steiner tree problems to
be more difficult to solve when the tree diameter D is odd. In this paper, we provide an alternate modeling approach that views problems with odd diameters as the superposition
of two problems with even diameters. We show how to tighten the resulting formulation to develop a model with a stronger linear
programming relaxation. The linear programming gaps for the tightened model are very small, typically less than 0.5–, and
are usually one third to one tenth of the gaps of the best previous model described in Gouveia and Magnanti (2003). Moreover,
the new model permits us to solve large Euclidean problem instances that are not solvable by prior approaches.
Research funded in part by the Research Projects POCTI-ISFL-1-152,POSI/CPS/41459/2001 and POCTI/MAT/139/94
Research funded in part by the Singapore-MITAlliance(SMA) 相似文献
74.
This paper presents a comprehensive review of the work done, during the 1968–2005, in the application of statistical and intelligent techniques to solve the bankruptcy prediction problem faced by banks and firms. The review is categorized by taking the type of technique applied to solve this problem as an important dimension. Accordingly, the papers are grouped in the following families of techniques: (i) statistical techniques, (ii) neural networks, (iii) case-based reasoning, (iv) decision trees, (iv) operational research, (v) evolutionary approaches, (vi) rough set based techniques, (vii) other techniques subsuming fuzzy logic, support vector machine and isotonic separation and (viii) soft computing subsuming seamless hybridization of all the above-mentioned techniques. Of particular significance is that in each paper, the review highlights the source of data sets, financial ratios used, country of origin, time line of study and the comparative performance of techniques in terms of prediction accuracy wherever available. The review also lists some important directions for future research. 相似文献
75.
Applicants for credit have to provide information for the risk assessment process. In the current conditions of a saturated consumer lending market, and hence falling “take” rates, can such information be used to assess the probability of a customer accepting the offer? 相似文献
76.
Optimal competence set expansion using deduction graphs 总被引:1,自引:0,他引:1
A competence set is a collection of skills used to solve a problem. Based on deduction graph concepts, this paper proposes a method of finding an optimal process so as to expand a decision maker's competence set to enable him to solve his problem confidently. Using the concept of minimum spanning tree, Yu and Zhang addressed the problem of the optimal expansion of competence sets. In contrast, the method proposed here enjoys the following advantages: it can deal with more general problems involving intermediate skills and compound skills; it can find the optimal solution by utilizing a 0–1 integer program; and it can be directly extended to treat multilevel competence set problems, and thus is more practically useful.This work was supported by the National Science Council, Taipei, Taiwan, Republic of China, Grant No. NSC-81-0301-H-009-501. 相似文献
77.
On spanning tree problems with multiple objectives 总被引:4,自引:0,他引:4
We investigate two versions of multiple objective minimum spanning tree problems defined on a network with vectorial weights. First, we want to minimize the maximum ofQ linear objective functions taken over the set of all spanning trees (max-linear spanning tree problem, ML-ST). Secondly, we look for efficient spanning trees (multi-criteria spanning tree problem, MC-ST).Problem ML-ST is shown to be NP-complete. An exact algorithm which is based on ranking is presented. The procedure can also be used as an approximation scheme. For solving the bicriterion MC-ST, which in the worst case may have an exponential number of efficient trees, a two-phase procedure is presented. Based on the computation of extremal efficient spanning trees we use neighbourhood search to determine a sequence of solutions with the property that the distance between two consecutive solutions is less than a given accuracy.Partially supported by Deutsche Forschungsgemeinschaft and HCº Contract no. ERBCHRXCT 930087.Partially supported by Alexander von Humboldt-Stiftung. 相似文献
78.
Based on uniform recursive trees, we introduce random trees with the factor of time, which are named Yule recursive trees. The structure and the distance between the vertices in Yule recursive trees are investigated in this paper. For arbitrary time t > 0, we first give the probability that a Yule recursive tree Yt is isomorphic to a given rooted tree γ; and then prove that the asymptotic distribution of ζt,m, the number of the branches of size m, is the Poisson distribution with parameter λ = 1/m. Finally, two types of distance between vertices in Yule recursive trees are studied, and some limit theorems for them are established.© 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2007 相似文献
79.
Simply generated families of trees are described by the equation T(z) = ϕ(T(z)) for their generating function. If a tree has n nodes, we say that it is increasing if each node has a label ∈ { 1,…,n}, no label occurs twice, and whenever we proceed from the root to a leaf, the labels are increasing. This leads to the concept of simple families of increasing trees. Three such families are especially important: recursive trees, heap ordered trees, and binary increasing trees. They belong to the subclass of very simple families of increasing trees, which can be characterized in 3 different ways. This paper contains results about these families as well as about polynomial families (the function ϕ(u) is just a polynomial). The random variable of interest is the level of the node (labelled) j, in random trees of size n ≥ j. For very simple families, this is independent of n, and the limiting distribution is Gaussian. For polynomial families, we can prove this as well for j,n → ∞ such that n − j is fixed. Additional results are also given. These results follow from the study of certain trivariate generating functions and Hwang's quasi power theorem. They unify and extend earlier results by Devroye, Mahmoud, and others. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2007 相似文献
80.
F. Fu L.-H. Liu L. Wang 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,56(4):367-372
We focus on the heterogeneity of social networks and its
role to the emergence of prevailing cooperators and sustainable
cooperation. The social networks are representative of the
interaction relationships between players and their encounters in
each round of games. We study an evolutionary Prisoner's Dilemma
game on a variant of Newman-Watts small-world network, whose
heterogeneity can be tuned by a parameter. It is found that
optimal cooperation level exists at some intermediate topological
heterogeneity for different temptations to defect. That is,
frequency of cooperators peaks at a certain specific value of
degree heterogeneity — neither the most heterogeneous case nor
the most homogeneous one would favor the cooperators. Besides, the
average degree of networks and the adopted update rule also affect
the cooperation level. 相似文献