A t-ary tree is a rooted tree such that every internal node has exactly t disjoint subtrees. Recently, a concise representation called right-distance sequences (RD-sequences) was introduced to represent t-ary trees and their generalization called non-regular trees. In particular, a loopless algorithm has been proposed by Wu et al. ((2010) Loopless generation of non-regular trees with a prescribed branching sequence. Comput. J., 53, 661–666) for generating non-regular trees (and thus of t-ary trees) encoded by RD-sequences in a Gray-code order. In this paper, based on such a Gray-code order, we present efficient ranking and unranking algorithms of t-ary trees with n internal nodes. The time complexity and space requirement in both algorithms are O(max{n2,tn}) and O(tn), respectively. As a by-product, we have an improvement on ranking and unranking t-ary trees encoded by z-sequences in a Gray-code order.

Abstract In this paper, the channel characteristics of ultra‐wideband systems with single co‐channel interference are investigated. A ray‐tracing technique is developed to calculate channel frequency responses in an indoor environment, of which the frequency dependence for the dielectric constant and the conductivity are carefully considered. By using the frequency responses, the channel capacities with single co‐channel interference are calculated. The outage probability of the channel capacities are also calculated for analyzing the channel statistical property. Furthermore, some useful channel statistical parameters are also investigated for different material partitions. Copyright © 2011 John Wiley & Sons, Ltd.

Graph visualization has been widely used to understand and present both global structural and local adjacency information in relational data sets (e.g., transportation networks, citation networks, or social networks). Graphs with dense edges, however, are difficult to visualize because fast layout and good clarity are not always easily achieved. When the number of edges is large, edge bundling can be used to improve the clarity, but in many cases, the edges could be still too cluttered to permit correct interpretation of the relations between nodes. In this paper, we present an ambiguity-free edge-bundling method especially for improving local detailed view of a complex graph. Our method makes more efficient use of display space and supports detail-on-demand viewing through an interactive interface. We demonstrate the effectiveness of our method with public coauthorship network data.