At the end of the last century, C. J. Yoccoz is made significant contributions to the theory of complex dynamics, one of which is the study of the local connectivity of the Julia sets of quadratic polynomials pc(z) = z2 + c and the Mandelbrot set M. In his work.

This paper first reviews AODV routing protocol briefly and introduces its two different mechanisms maintaining local connectivity: Link layer mechanism based on Cross-Layer Design and Network layer mechanism, then compares the performance of AODV routing protocol under these two mechanisms through NS2, and points out the merits and demerits between them.

In addition, it is proved that the two kinds of algorithms based on local weak-connectivity concepts are extensions of the algorithms based on the two kinds of local connectivity concepts.

Furthermore ,there exists Y_3 V_3-free graphs with arbitrarily high connectivity and local connectivity which are nonhamiltonian. The research of the longest cycles will promote the Hamitonian Problem research.

The CNN silicon integration success is due mainly to the local connectivity of processing cells.

The systolic array has advantages of pipelinability, regularity, modularity, local connectivity and scalability, thus making it to be very suitable for VLSI implementation.

We present a new description of ordering and phase transitions in terms of genuine local connectivity, i.e., physical connections and disconnections which lead to global order and disorder, respectively.

Description of ordering and phase transitions in terms of local connectivity: Proof of a novel type of percolated state in the g

In fact, their regular structure and their local connectivity feature contribute to render this class of neural networks especially appealing for VLSI implementations.

The concepts of local connectivity of single-value mappings and peripherally continu- ous mapping are extended to set-value.The condition is given in which set-value peripheri- ally mapping is set-value local connecting mappings.

Routing has been a popular topic in the study of computer networks. With the continuous increasing in network size, routing in large size networks with faults has become unavoidable. We introduce a new and natural concept of fault tolerance for hypercube networks: local-connectivity. Two kinds of local-connectivity have been defined in this paper. The first kind of local-connectivity is local k-subcube-connectivity, in which each k-dimensional subcube H k contains...

Routing has been a popular topic in the study of computer networks. With the continuous increasing in network size, routing in large size networks with faults has become unavoidable. We introduce a new and natural concept of fault tolerance for hypercube networks: local-connectivity. Two kinds of local-connectivity have been defined in this paper. The first kind of local-connectivity is local k-subcube-connectivity, in which each k-dimensional subcube H k contains less than 2 k-1 faulty nodes and the non-faulty nodes in H k make a connected graph. The second kind of local-connectivity is local subcube-connectivity, in which if for every k-dimensional subcube H k of H n, where k1, there is an h-dimensional subcube H h containing H k (thus hk) such that H h is locally h-subcube connected. We show that a locally connected hypercube network may contain a large number of faulty nodes, and prove that a locally connected hypercube network is also globally connected. We develop two efficient routing algorithms on locally connected hypercube networks: for a locally k-subcube-connected n-dimensional hypercube network H n, our first routing algorithm constructs a path of non-faulty nodes from a given source node to a given destination node in time O(n2k); for a locally subcube-connected n-dimensional hypercube network H n, our second routing algorithm constructs a path of non-faulty nodes from a given source node to a given destination node in time O(n2 k min), where k min is the smallest integer such that the n-dimensional hypercube H n is locally k min-subcube-connected (where the value k min is not necessarily known to our algorithm)/ Our routing algorithms are distributed and local-information-based in the sense that each node in the network knows only its neighbors' status and no global information of the network is required by the algorithms. Our new concept of local-connectivity is easily extendable to other hierarchical networks. Finally, other network problems, such as network emulation and network broadcasting, should also be interesting under our new concept of local-connectivity.

Parallel fault tolerant routing algorithms in hypercube networks with a large number of faulty nodes are studied. Using experimental results, the fault tolerance and effectiveness and efficiency of parallel fault tolerant routing algorithm are analysed, which is based on both locally k subcube connected fault tolerant model and locally 3 subcube connected fault tolerant model with up to 25.0% faulty nodes. It is well known that the number of parallel paths which can be found by a parallel routing algorithm...

Parallel fault tolerant routing algorithms in hypercube networks with a large number of faulty nodes are studied. Using experimental results, the fault tolerance and effectiveness and efficiency of parallel fault tolerant routing algorithm are analysed, which is based on both locally k subcube connected fault tolerant model and locally 3 subcube connected fault tolerant model with up to 25.0% faulty nodes. It is well known that the number of parallel paths which can be found by a parallel routing algorithm is at most min( D(u),D(v) ), and at least min (D k(u),D k(v)) . Considering that k is small (such as 3, 4 or 5), and that n is large (such as 10, 15, 20 or 30), then min (D(u),D(v) ) is very close to min (D k(u),D k(v) ). In this way, the capability of finding the parallel routing paths as much as possible is near optimal. The theoretical analysis and the experimental results show that not only parallel routing algorithms are strong fault tolerant and highly effective and efficient, but also local connectivity fault tolerant model is applicable.