SUMMARYThe topology of interconnection networks plays an important role in the performance of parallel and distributed computing systems. In this paper, we propose a new interconnection network called twisted crossed cube (TCQ n ) and investigate its basic network properties in terms of the regularity, connectivity, fault tolerance, recursiveness, hamiltonicity and ability to simulate other architectures, and so on. Then, we develop an effective routing algorithm Route (u, v) for TCQ n that takes no more than d(u, v) + 1 steps for any two nodes (u, v) to communicate with each other, and the routing process shows that the diameter, wide diameter, and fault-tolerant diameter of TCQ n are about half of the corresponding diameters of the equivalent hypercube with the same dimension. In the end, by combining TCQ n with crossed cube (CQ n ), we propose a preferable dynamic network structure, that is, the dynamic crossed cube, which has the same network diameter as TCQ n /CQ n and better properties in other respects, for example, its connection complexity is half of that of TCQ n /CQ n when the network scale is large enough, and the number of its average routing steps is also much smaller than that in TCQ n /CQ n .
This paper studies the weighted average consensus problem for networks of agents with xed directed asymmetric unbalance information exchange topology. We suppose that the classical distributed consensus protocol is destroyed by diverse time-delays which include communication time-delay and self time-delay. Based on the generalized Nyquist stability criterion and the Gerschgorin disk theorem, some suf cient conditions for the consensus of multi-agent systems are obtained. And we give the expression of the weighted average consensus value for our consensus protocol. Finally, numerical examples are presented to illustrate the theoretical results.
In a wireless ad hoc network, the size of the virtual backbone (VB) is an important factor for measuring the quality of the VB. The smaller the VB is, the less the overhead caused by the VB. Since ball graphs (BGs) have been used to model 3-dimensional wireless ad hoc networks and since a connected dominating set can be used to represent a VB undertaking routing-related tasks, the problem of finding the smallest VB is transformed into the problem of finding a minimum connected dominating set (MCDS). Many research results on the MCDS problem have been obtained for unit disk graphs and unit ball graphs, in which the transmission ranges of all nodes are identical. In some situations, the node powers can vary. One can model such a network as a graph with different transmission ranges for different nodes. In this paper, we focus on the problem of minimum strongly connected dominating and absorbing sets (MSCDASs) in a strongly connected directed ball graph with different transmission ranges, which is also NP-hard. We design an algorithm considering the construction of a strongly connected dominating and absorbing set (SCDAS), whose size does not exceed 319/15k3+116/5k2+29/5kopt+29/3k3+116/5k2+87/5k+13/15, where opt is the size of an MCDAS and k denotes the ratio of rmax to rmin in the ad hoc network with transmission range rmin,rmax. Our simulations show the feasibility of the algorithm proposed in this paper.
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