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41.
凸集的广义Reuleaux三角形 总被引:1,自引:1,他引:0
常宽凸集的面积最小者为Reulaux三角形,而非常宽凸集的面积最小者为何呢?它就是本文将给出的广义Reuleaux三角形△R。 相似文献
42.
43.
Chepoi showed that every breadth first search of a bridged graph produces a cop-win ordering of the graph. We note here that Chepoi's proof gives a simple proof of the theorem that G is bridged if and only if G is cop-win and has no induced cycle of length four or five, and that this characterization together with Chepoi's proof reduces the time complexity of bridged graph recognition. Specifically, we show that bridged graph recognition is equivalent to (C4,C5)-free graph recognition, and reduce the best known time complexity from O(n4) to O(n3.376). 相似文献
44.
In this paper we construct the linear support vector machine (SVM) based on the nonlinear rescaling (NR) methodology (see
[Polyak in Math Program 54:177–222, 1992; Polyak in Math Program Ser A 92:197–235, 2002; Polyak and Teboulle in Math Program
76:265–284, 1997] and references therein). The formulation of the linear SVM based on the NR method leads to an algorithm
which reduces the number of support vectors without compromising the classification performance compared to the linear soft-margin
SVM formulation. The NR algorithm computes both the primal and the dual approximation at each step. The dual variables associated
with the given data-set provide important information about each data point and play the key role in selecting the set of
support vectors. Experimental results on ten benchmark classification problems show that the NR formulation is feasible. The
quality of discrimination, in most instances, is comparable to the linear soft-margin SVM while the number of support vectors
in several instances were substantially reduced. 相似文献
45.
A (p, q)-sigraph S is an ordered pair (G, s) where G = (V, E) is a (p, q)-graph and s is a function which assigns to each edge of G a positive or a negative sign. Let the sets E
+ and E
– consist of m positive and n negative edges of G, respectively, where m + n = q. Given positive integers k and d, S is said to be (k, d)-graceful if the vertices of G can be labeled with distinct integers from the set {0, 1, ..., k + (q – 1)d such that when each edge uv of G is assigned the product of its sign and the absolute difference of the integers assigned to u and v the edges in E
+ and E
– are labeled k, k + d, k + 2d, ..., k + (m – 1)d and –k, – (k + d), – (k + 2d), ..., – (k + (n – 1)d), respectively.In this paper, we report results of our preliminary investigation on the above new notion, which indeed generalises the well-known concept of (k, d)-graceful graphs due to B. D. Acharya and S. M. Hegde. 相似文献
46.
Let G = (V,E) be a graph or digraph and r : V → Z+. An r‐detachment of G is a graph H obtained by ‘splitting’ each vertex ν ∈ V into r(ν) vertices. The vertices ν1,…,νr(ν) obtained by splitting ν are called the pieces of ν in H. Every edge uν ∈ E corresponds to an edge of H connecting some piece of u to some piece of ν. Crispin Nash‐Williams 9 gave necessary and sufficient conditions for a graph to have a k‐edge‐connected r‐detachment. He also solved the version where the degrees of all the pieces are specified. In this paper, we solve the same problems for directed graphs. We also give a simple and self‐contained new proof for the undirected result. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 67–77, 2003 相似文献
47.
For each infinite cardinal κ, we give examples of 2κ many non‐isomorphic vertex‐transitive graphs of order κ that are pairwise isomorphic to induced subgraphs of each other. We consider examples of graphs with these properties that are also universal, in the sense that they embed all graphs with smaller orders as induced subgraphs. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 99–106, 2003 相似文献
48.
Jochen Alber Jií Fiala 《Journal of Algorithms in Cognition, Informatics and Logic》2004,52(2):134-151
We consider the parameterized problem, whether for a given set
of n disks (of bounded radius ratio) in the Euclidean plane there exists a set of k non-intersecting disks. For this problem, we expose an algorithm running in time
that is—to our knowledge—the first algorithm with running time bounded by an exponential with a sublinear exponent. For λ-precision disk graphs of bounded radius ratio, we show that the problem is fixed parameter tractable with a running time
. The results are based on problem kernelization and a new “geometric (
-separator) theorem” which holds for all disk graphs of bounded radius ratio. The presented algorithm then performs, in a first step, a “geometric problem kernelization” and, in a second step, uses divide-and-conquer based on our new “geometric separator theorem.” 相似文献
49.
Alexander Koldobsky 《Advances in Applied Mathematics》2004,33(4):728-732
The Busemann–Petty problem asks whether origin-symmetric convex bodies in Rn with smaller areas of all central hyperplane sections necessarily have smaller n-dimensional volume. The solution was completed in the end of the 1990s, and the answer is affirmative if n4 and negative if n5. Since the answer is negative in most dimensions, it is natural to ask what information about the volumes of central sections of two bodies does allow to compare the n-dimensional volumes of these bodies in all dimensions. In this article we give an answer to this question in terms of certain powers of the Laplace operator applied to the section function of the body. 相似文献
50.
PSN is a fast forward permutation if for each m the computational complexity of evaluating Pm(x) is small independently of m and x. Naor and Reingold constructed fast forward pseudorandom cycluses and involutions. By studying the evolution of permutation graphs, we prove that the number of queries needed to distinguish a random cyclus from a random permutation in SN is Θ(N) if one does not use queries of the form Pm(x), but is only Θ(1) if one is allowed to make such queries. We construct fast forward permutations which are indistinguishable from random permutations even when queries of the form Pm(x) are allowed. This is done by introducing an efficient method to sample the cycle structure of a random permutation, which in turn solves an open problem of Naor and Reingold. 相似文献