An AVL tree [1] is the original type of balanced binary search tree. An insertion in an n-node AVL tree takes at most two rotations, but a deletion in an n-node AVL tree can take Θ(log n). A natural question is whether deletions can take many rotations not only in the worst case but in the amortized case as well. A sequence of n successive deletions in an n-node tree takes O(n) rotations [3], b...

Developing a Tree Adjoining Grammar which contains the information necessary for building the basic compositional semantics of sentences is a highly complex engineering task. To ensure consistency, ease of writing, of maintainance and of debugging, it is therefore important that this information be described at the appropriate level of abstraction. In the first part of this paper (sections 2 an...

This survey describes the contribution of N. Aronszajn to set theory: the construction of an Aronszajn tree. We would like to explain to the non-specialist in set theory what is an Aronszajn tree, how it is constructed, and why it occupies such a central place in set theory. In fact, we describe two constructions: the classical one, and a newer construction of a canonical Aronszajn tree due to ...

The classification-tree method developed by Grochtmann and Grimm facilitates the identification of test cases from functional specifications via the construction of classification trees. Their method has been enhanced by Chen and Poon through the classification-tree construction and restructuring methodologies. We find, however, that the restructuring algorithm by Chen and Poon is applicable on...

We propose an hybrid CPU-GPU ray-tracing implementation based on an optimal Kd-Tree as acceleration structure. The construction and traversal of this KD-tree takes benefit from both the CPU and the GPU to achieve high-performance ray-tracing on mainstream hardware. Our approach, flexible enough to use only a single computing unit (CPU or GPU), is able to efficiently distribute workload between ...

This article recommends a practical technique to design full chip (FC) clock tree of complex system-on-chip (SoC). In the new business environment, market prefers highly integrated but low power SoC with fast productivity and development cost. We observed that many techniques proposed in prior arts are no longer or enough. With that, we introduce flexible FC Clock network topology synthesis alg...

The circular orders associated with planar drawings of an X-tree (or phylogenetic tree) have been studied by several authors, especially for the encoding of an X-tree by 2n-3 lengths of paths between leaves (n being the cardinality of X). It is shown here that circular orders are the same as those obtained from the table of a tree metric by a construction due to Yushmanov (1984). More, this con...

Accumulation of complete genome sequences of diverse organisms creates new possibilities for evolutionary inferences from whole-genome comparisons. In the present study, we analyze the distributions of substitution rates among proteins encoded in 19 complete genomes (the interprotein rate distribution). To estimate these rates, it is necessary to employ another fundamental distribution, that of...

Cesium atomic beam clocks have been the workhorse for many demanding applications in science and technology for the past four decades. Tests of the fundamental laws of physics and the search for minute changes in fundamental constants, the synchronization of telecommunication networks, and realization of the satellite-based global positioning system would not be possible without atomic clocks. ...