A graph is said to be cyclic k-edge-connected, if at least k edges must be removed to disconnect it into two components, each containing a cycle. Such a set of k edges is called a cyclic-k-edge cutset and it is called a trivial cyclic-k-edge cutset if at least one of the resulting two components induces a single k-cycle. It is known that fullerenes, that is, 3-connected cubic planar graphs all ...

A snap-stabilizing protocol, starting from any configuration, always behaves according to its specification. In this paper, we present a snap-stabilizing protocol which detects if a set of processors is a cutset of an arbitrary rooted network. This protocol is based on the depth-first search ( ) traversal and its properties. An interesting property of our protocol is that, despite the initial c...

The minimum cut problem (or mincut problem) is to find a cut of minimum cost. If all costs are 1 then the problem becomes the problem of finding a cut with as few edges as possible. Cuts are often defined in a different, not completely equivalent, way. Define a cutset to be a set of edges whose removal disconnects the graph into at least two connected components. Minimal cutsets (a minimal cuts...

The complexity of the exact inference increases exponentially with size and complexity of the network. As a result, the exact inference methods become impractical for large networks and we seek to approximate the results. A variety of approximation methods exist. This research focuses on two approximation methods for finding posterior marginals P (xi|e) in Bayesian networks: iterative belief up...

Abstract Influenced by the continuous growth of renewable energy installation scale and increasingly prominent characteristics AC/DC hybrid structure, disturbance behavior large power grid is becoming more complex. To ensure safety grid, higher requirements are put forward for reliability, accuracy orderliness out-of-step splitting control which belonged to third line defense. Firstly, this pap...

In this article we study capacitated network design problems. We unify and extend poly-hedral results for directed, bidirected and undirected link capacity models. Based on validinequalities for a network cut we show that regardless of the link capacity model, facets of thepolyhedra associated with such a cut translate to facets of the original network design polyhedraif the...

The loop cutset solving algorithm in the Bayesian network is particularly important for inference. This paper proposes an approximate minimum based on loop-cutting contribution index. Compared with existing algorithms, uses index of nodes and node-pairs to analyze from a global perspective, select candidates node-pair as unit. parameter μ control range node-pairs, ω selection conditions so that...