Sentence examples for directed spanning from inspiring English sources
We prove that a necessary and sufficient condition for an appropriate decentralized linear stabilizing feedback to exist is that G has a rooted directed spanning tree.
Two kinds of general algebraic connectivity are introduced to respectively investigate the global consensus in strongly connected networks and a class of networks containing directed spanning trees.
In [28], the topologies switch periodically and some nodes are pinned all the time though the topologies contain no directed spanning tree.
Moreover, no node is pinned when the topologies contain no directed spanning tree and the pinned nodes are dependent on the topologies.
That is, for all (tin [tilde{t}_{k},tilde{s}_{k})), the network topologies contain a directed spanning tree, and for all (tin [tilde{s}_{k},tilde{t}_{k+1})), the network topologies contain no directed spanning tree. Moreover, ([tilde{t}_{k},tilde{s}_{k})) and ([tilde{s}_{k},tilde{t}_{k+1})) have no multiple switching.
It is easy to see that ({tilde{t}_{k},kgeq 0}) is the set of switching time containing directed spanning tree and ({tilde{s}_{k},kgeq 0}) is the set of switching time when the directed network does not contain any directed spanning tree.
The augmented graph contains a directed span tree rooted at the virtual node.
Briefly, a ShReD value (length of the shortest directed cycle spanning two reaction nodes) was computed for every reaction pair in the parent network.
The problems we study are the min-max variant of the shortest path and the (directed) minimum spanning tree mechanism design problems.
Then, the three main steps of the method are described: the skeleton extraction and pruning algorithm, the definition and computation of a travel cost between all pairs of skeleton vertices, and the identification of the directed minimum spanning tree in the resulting directed graph.
We focus on the analysis of connectivity properties in FSDNs and the design of algorithms for building directed minimal spanning trees (DMSTs) to generate multicast routes in FSDNs.
