共查询到19条相似文献,搜索用时 187 毫秒
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设G是一个图,f是定义在V(G)上的整数值函数,且对坌x∈V(G),有2k≤f(x),设H1,H2,…,Hk是G的k个顶点不相交的子图,且|E(Hi)|=m,1≤i≤k,证明了每个(0,mf-m+1)图有一个(0,f)因子分解正交于Hi(i=1,2,…,k)。 相似文献
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著名的Steiner树问题是,给定图G=(V、E),QV,在边集E上定义权函数f:E→Z~+,要求在图G上找一子树T=(Y,U),使得QY且 ∑_(c∈U)f(e)达到极小以后,我们称该问题为ST问题,R.M.Karp曾证明ST问题为NP-完全的,本文作者曾提出图上Steiner树问题:在图G=(V,E),QV上,要求一子树T=(Y, 相似文献
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微分几何方法与非线性控制系统(4) 总被引:4,自引:0,他引:4
7 非线性控制系统的几何理论 7.1 非线性控制系统的几何描述 定义在R~n上的一般非线性系统可以用微分方程描述如下: x=f(x,4) (7.1a) y=h(x) (7.1b)这里,状态x∈R~n;控制u∈R~m;输出y∈R~r,等式(7.1a)称为状态方程,(7.1b)称为输出方程。为了便于使用微分几何的工具,假设f对x和u都是光滑或解析函数,同样,h(x)也是C~∞ 相似文献
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1.图上STEINER树问题是NP-完全的 著名的网络上Steiner问题是:对给定图G=(V,E),其中V=PUS,在边集E(G)上定义权函数f:E(G)→Z~ ,构成网络N(G,f)。要求在网络N(G,f)上寻找一棵子树T=(Y,u),使得P(?)Y,且 相似文献
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图G的孤立韧度定义为I(G)=min{|S|/i(G-S):S!V(G),i(G-S)≥2},若G不是完全图;否则,令I(G)=∞。论文给出了图的分数[a,b]-因子的存在性与图的孤立韧度的关系。证明若δ(G)≥I(G)≥a-1+a/b,则图G有分数[a,b]-因子,其中a相似文献
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Let X /spl sub/ /spl Ropf//sup N/ and consider a system x/spl dot/ = f(x,u), f : X /spl times/ /spl Ropf//sup M/ /spl rarr/ /spl Ropf//sup N/, with the property that the associated autonomous system x/spl dot/ = f (x,0) has an asymptotically stable compactum C with region of attraction A. Assume that x is a solution of the former, defined on [0,/spl infin/), corresponding to an input function u. Assume further that, for each compact K /spl sub/ X, there exists k > 0 such that |f(z,v) - f(z,0)| /spl les/ k|v| for all (z,v) /spl isin/ /spl times/ /spl Ropf//sup M/. A simple proof is given of the following L/sup p/-input converging-state property: if u /spl isin/ L/sup p/ for some p /spl isin/ [1,/spl infin/) and x has an /spl omega/-limit point in A, then x approaches C. 相似文献
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张国珍 《计算机工程与应用》2017,53(8):19-22
限制边连通度是度量网络可靠性的重要参数。设[G]是一个边集为[E]的连通网络。称一个边集合[S?E]是一个限制边割,如果[G-S]是不连通的且每个分支至少有两个顶点。网络[G]的限制边连通度,记为[λ'],定义为[G]的最小限制边割的基数。设[d(v)]表示顶点[v]的度,[ξ=min{d(u)+d(v)-2:uv∈E}]表示[G]的最小边度。称网络[G]是极大限制边连通的,如果[λ'=ξ]。给出了网络是极大限制边连通的一些充分条件。 相似文献
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Let $G=(V,E)$ be an undirected multigraph with a special vertex
${\it root} \in V$, and where each edge $e \in E$ is endowed with a
length $l(e) \geq 0$ and a capacity $c(e) > 0$. For a path $P$
that connects $u$ and $v$, the {\it transmission time} of $P$ is
defined as $t(P)=\mbox{\large$\Sigma$}_{e \in P} l(e) + \max_{e \in P}\!{(1 /
c(e))}$. For a spanning tree $T$, let $P_{u,v}^T$ be the unique $u$--$v$
path in $T$. The {\sc quickest radius spanning tree problem} is to find
a spanning tree $T$ of $G$ such that $\max _{v \in V} t(P^T_{root,v})$ is
minimized. In this paper we present a 2-approximation algorithm for
this problem, and show that unless $P =NP$, there is no approximation
algorithm with a performance guarantee of $2 - \epsilon$ for any
$\epsilon >0$. The {\sc quickest diameter spanning tree problem} is
to find a spanning tree $T$ of $G$ such that $\max_{u,v \in V}
t(P^T_{u,v})$ is minimized. We present a ${3 \over 2}$-approximation
to this problem, and prove that unless $P=NP$
there is no approximation algorithm with a performance guarantee of
${3 \over 2}-\epsilon$ for any $\epsilon >0$. 相似文献
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Let $G=(V,E)$ be an undirected multigraph with a special vertex
${\it root} \in V$, and where each edge $e \in E$ is endowed with a
length $l(e) \geq 0$ and a capacity $c(e) > 0$. For a path $P$
that connects $u$ and $v$, the {\it transmission time} of $P$ is
defined as $t(P)=\mbox{\large$\Sigma$}_{e \in P} l(e) + \max_{e \in P}\!{(1 /
c(e))}$. For a spanning tree $T$, let $P_{u,v}^T$ be the unique $u$--$v$
path in $T$. The {\sc quickest radius spanning tree problem} is to find
a spanning tree $T$ of $G$ such that $\max _{v \in V} t(P^T_{root,v})$ is
minimized. In this paper we present a 2-approximation algorithm for
this problem, and show that unless $P =NP$, there is no approximation
algorithm with a performance guarantee of $2 - \epsilon$ for any
$\epsilon >0$. The {\sc quickest diameter spanning tree problem} is
to find a spanning tree $T$ of $G$ such that $\max_{u,v \in V}
t(P^T_{u,v})$ is minimized. We present a ${3 \over 2}$-approximation
to this problem, and prove that unless $P=NP$
there is no approximation algorithm with a performance guarantee of
${3 \over 2}-\epsilon$ for any $\epsilon >0$. 相似文献
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Bertossi A.A. Pinotti C.M. Tan R.B. 《Parallel and Distributed Systems, IEEE Transactions on》2003,14(3):222-235
Given an integer /spl sigma/>1, a vector (/spl delta//sub 1/, /spl delta//sub 2/,..., /spl delta//sub /spl sigma/-1/), of nonnegative integers, and an undirected graph G=(V, E), an L(/spl delta//sub 1/, /spl delta//sub 2/,..., /spl delta//sub /spl sigma/-1/)-coloring of G is a function f from the vertex set V to a set of nonnegative integers, such that |f(u)-f(v)|/spl ges//spl delta//sub i/, if d(u,v)=i, for 1相似文献
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Yuichi Yoshida 《Computational Complexity》2016,25(4):737-773
In the List H- Homomorphism Problem, for a graph H that is a parameter of the problem, an instance consists of an undirected graph G with a list constraint \({L(v) \subseteq V(H)}\) for each variable \({v \in V(G)}\), and the objective is to determine whether there is a list H-homomorphism \({f:V(G) \to V(H)}\), that is, \({f(v) \in L(v)}\) for every \({v \in V(G)}\) and \({(f(u),f(v)) \in E(H)}\) whenever \({(u,v) \in E(G)}\).We consider the problem of testing list H-homomorphisms in the following weighted setting: An instance consists of an undirected graph G, list constraints L, weights imposed on the vertices of G, and a map \({f:V(G) \to V(H)}\) given as an oracle access. The objective is to determine whether f is a list H-homomorphism or far from any list H-homomorphism. The farness is measured by the total weight of vertices \({v \in V(G)}\) for which f(v) must be changed so as to make f a list H-homomorphism. In this paper, we classify graphs H with respect to the number of queries to f required to test the list H-homomorphisms. Specifically, we show that (i) list H-homomorphisms are testable with a constant number of queries if and only if H is a reflexive complete graph or an irreflexive complete bipartite graph and (ii) list H-homomorphisms are testable with a sublinear number of queries if and only if H is a bi-arc graph. 相似文献
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J. B. Kioustelidis 《Computing》1989,43(2):133-140
New a posteriori (computable) upper bounds for theL 2-norms, both ofD(u?v) and ofu?v are proposed, whereu is the exact solution of the boundary value problem $$Au: = - D(pDu) + qu = f, x \in G and u = 0,x \in \partial G$$ andv any approximation of it (D is here the vector of partial derivatives with respect to the components ofx). It is shown that the new error bounds are better than the classical one, which is proportional to ‖Av?f‖, in many cases. This happens, e. g., ifq has some zero point inG, as in the case of a Poisson equation. 相似文献
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Shan-Chyun Ku Biing-Feng Wang Ting-Kai Hung 《Parallel and Distributed Systems, IEEE Transactions on》2003,14(3):213-221
A Cartesian product network is obtained by applying the cross operation on two graphs. We study the problem of constructing the maximum number of edge-disjoint spanning trees (abbreviated to EDSTs) in Cartesian product networks. Let G=(V/sub G/, E/sub G/) be a graph having n/sub 1/ EDSTs and F=(V/sub F/, E/sub F/) be a graph having n/sub 2/ EDSTs. Two methods are proposed for constructing EDSTs in the Cartesian product of G and F, denoted by G/spl times/F. The graph G has t/sub 1/=|E/sub G/|/spl middot/n/sub 1/(|V/sub G/|-1) more edges than that are necessary for constructing n/sub 1/ EDSTs in it, and the graph F has t2=|E/sub F/'-n/sub 2/(|V/sub F/|-1) more edges than that are necessary for constructing n/sub 2/ EDSTs in it. By assuming that t/sub 1//spl ges/n/sub 1/ and t/sub 2//spl ges/n/sub 2/, our first construction shows that n/sub 1/+n/sub 2/ EDSTS can be constructed in G/spl times/F. Our second construction does not need any assumption and it constructs n/sub 1/+n/sub 2/-1 EDSTs in G/spl times/F. By applying the proposed methods, it is easy to construct the maximum numbers of EDSTs in many important Cartesian product networks, such as hypercubes, tori, generalized hypercubes, mesh connected trees, and hyper Petersen networks. 相似文献