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51.
Brian Lucena 《Discrete Applied Mathematics》2007,155(8):1055-1065
One consequence of the graph minor theorem is that for every k there exists a finite obstruction set Obs(TW?k). However, relatively little is known about these sets, and very few general obstructions are known. The ones that are known are the cliques, and graphs which are formed by removing a few edges from a clique. This paper gives several general constructions of minimal forbidden minors which are sparse in the sense that the ratio of the treewidth to the number of vertices n does not approach 1 as n approaches infinity. We accomplish this by a novel combination of using brambles to provide lower bounds and achievable sets to demonstrate upper bounds. Additionally, we determine the exact treewidth of other basic graph constructions which are not minimal forbidden minors. 相似文献
52.
Many recent algorithmic approaches involve the construction of a differential equation model for computational purposes, typically
by introducing an artificial time variable. The actual computational model involves a discretization of the now time-dependent differential system, usually
employing forward Euler. The resulting dynamics of such an algorithm is then a discrete dynamics, and it is expected to be
“close enough” to the dynamics of the continuous system (which is typically easier to analyze) provided that small – hence
many – time steps, or iterations, are taken. Indeed, recent papers in inverse problems and image processing routinely report
results requiring thousands of iterations to converge. This makes one wonder if and how the computational modeling process
can be improved to better reflect the actual properties sought.
In this article we elaborate on several problem instances that illustrate the above observations. Algorithms may often lend
themselves to a dual interpretation, in terms of a simply discretized differential equation with artificial time and in terms
of a simple optimization algorithm; such a dual interpretation can be advantageous. We show how a broader computational modeling
approach may possibly lead to algorithms with improved efficiency.
AMS subject classification (2000) 65L05, 65M32, 65N21, 65N22, 65D18 相似文献
53.
54.
E. Mathieu Y. Foucher P. Dellamonica J. P. Daures 《Methodology and Computing in Applied Probability》2007,9(3):389-397
In AIDS control, physicians have a growing need to use pragmatically useful and interpretable tools in their daily medical
taking care of patients. Semi-Markov process seems to be well adapted to model the evolution of HIV-1 infected patients. In
this study, we introduce and define a non homogeneous semi-Markov (NHSM) model in continuous time. Then the problem of finding
the equations that describe the biological evolution of patient is studied and the interval transition probabilities are computed.
A parametric approach is used and the maximum likelihood estimators of the process are given. A Monte Carlo algorithm is presented
for realizing non homogeneous semi-Markov trajectories. As results, interval transition probabilities are computed for distinct
times and follow-up has an impact on the evolution of patients.
相似文献
55.
对覆盖广义Rough集中的隶属关系、隶属函数进行了定义,并利用隶属函数定义了集合的Rough包含与Rough相等,得到一些与Pawlak的Rough集不同的性质。 相似文献
56.
Yuanqiu Huang 《Discrete Applied Mathematics》2007,155(3):405-409
A stable set of a graph is a vertex set in which any two vertices are not adjacent. It was proven in [A. Brandstädt, V.B. Le, T. Szymczak, The complexity of some problems related to graph 3-colorability, Discrete Appl. Math. 89 (1998) 59-73] that the following problem is NP-complete: Given a bipartite graph G, check whether G has a stable set S such thatG-Sis a tree. In this paper we prove the following problem is polynomially solvable: Given a graph G with maximum degree 3 and containing no vertices of degree 2, check whether G has a stable set S such thatG-Sis a tree. Thus we partly answer a question posed by the authors in the above paper. Moreover, we give some structural characterizations for a graph G with maximum degree 3 that has a stable set S such that G-S is a tree. 相似文献
57.
基于Ritt-Wu特征集方法和Riquier-Janet理论,给出一种将线性微分方程组化成简单标准形式的有效算法.该算法通过消去冗余和添加可积条件获得线性微分方程组的完全可积系统(有形式幂级数解)或不相容判定.该算法不仅适用于常系数的线性偏微分方程组,而且对于变系数(以函数为系数)仍然有效.作者还给出了完全可积系统判定定理及其严格证明. 相似文献
58.
Marion SCHEEPERS 《数学学报(英文版)》2007,23(7):1153-1162
We show that a set of real numbers is a Sierpinski set if, and only if, it satisfies a selection property similar to the familiar Menger property. 相似文献
59.
We construct a new family of cyclic difference sets with parameters ((3
d
– 1)/2, (3
d – 1 – 1)/2, (3
d – 2 – 1)/2) for each odd d. The difference sets are constructed with certain maps that form Jacobi sums. These new difference sets are similar to Maschietti's hyperoval difference sets, of the Segre type, in characteristic two. We conclude by calculating the 3-ranks of the new difference sets. 相似文献
60.
In this paper, we introduce a new concept of semi-preemptive scheduling and we show how it can be used to derive a maximum-flow-based lower bound for the P|rj|Lmax which dominates the well-known preemptive lower bound. We show that, in some cases, the proposed bound strictly dominates the preemptive one while having the same complexity. 相似文献