A Framework for Index Bulk Loading and Dynamization

In this paper we investigate automated methods for externalizing internal memory data structures. We consider a class of balanced trees that we call weight-balanced partitioning trees (or wp-trees) for indexing a set of points in Rd. Well-known examples of wp-trees include fed-trees, BBD-trees, pseudo quad trees, and BAR trees. These trees are defined with fixed degree and are thus suited for internal memory implementations. Given an efficient wp-tree construction algorithm, we present a general framework for automatically obtaining a new dynamic external data structure. Using this framework together with a new general construction (bulk loading) technique of independent interest, we obtain data structures with guaranteed good update performance in terms of I /O transfers. Our approach gives considerably improved construction and update I/O bounds of e.g. fed-trees and BBD-trees

Fully dynamic maintenance of euclidean minimum spanning trees

We maintain the minimum spanning tree of a point set in the plane, subject to point insertions and deletions, in time O(n^5/6 log1^2/2 n) per update operation. No nontrivial dynamic geometric minimum spanning tree algorithm was previously known. We reduce the problem to maintaining bichromatic closest pairs, which we also solve in the same time bounds. Our algorithm uses a novel construction, the ordered nearest neighbors of a sequence of points. Any point set or bichromatic point set can be ordered so that this graph is a simple path

A technique for adding range restrictions to generalized searching problems

In a generalized searching problem, a set $S$ of $n$ colored geometric objects has to be stored in a data structure, such that for any given query object $q$, the distinct colors of the objects of $S$ intersected by $q$ can be reported efficiently. In this paper, a general technique is presented for adding a range restriction to such a problem. The technique is applied to the problem of querying a set of colored points (resp.\ fat triangles) with a fat triangle (resp.\ point). For both problems, a data structure is obtained having size $O(n^{1+\epsilon})$ and query time $O((\log n)^2 + C)$. Here, $C$ denotes the number of colors reported by the query, and $\epsilon$ is an arbitrarily small positive constant

Developments in circular external fixators: a review

Circular external fixators (CEFs) are successfully used in orthopedics owing to their highly favorable stiffness characteristics which promote distraction osteogenesis. Although there are different designs of external fixators, how these features produce optimal biomechanics through structural and component designs is not well known. Therefore, the aim of this study was to conduct a review on CEFs following the PRISMA statement. A search for relevant research articles was performed on Scopus and PubMed databases providing the related keywords. Furthermore, a patent search was conducted on the Google Patent database. 126 records were found to be eligible for the review. Different designs of CEFs were summarized and tabulated based on their specific features. A bibliometric analysis was also performed on the eligible research papers. Based on the findings, the developments of CEFs in terms of materials, automation, adjustment methods, component designs, wire-clamping, and performance evaluation have been extensively discussed. The trends of the CEF design and future directions are also discussed in this review. Significant research gaps include a lack of consideration towards ease of assembly, effective wire-clamping methods, and CEFs embedded with online patient-monitoring systems, among others. An apparent lack of research interest from low-middle and low-income countries was also identified