2 External-Memory Sorting

This lecture will cover sorting in the cache-oblivious world. Sorting seems like an unusual topic for a data structures course, but as we will see, the results of our discussion of cache-oblivious sorting will lead to our development of cache-oblivious priority queues. We first review external-memory sorting before moving on to cache-oblivious sorting, priority queues, and Funnel Heaps. 1.1 Notation This lecture uses capital letters in our analysis. We choose this notation because some papers use the notation n = N M B and m = B, where N is the number of elements, M is the size of the cache, and B is the block size. This notation is confusing so we will avoid it

Measuring Scanner Dynamic Range Different Methods

The use of scanners to provide digital image files is rapidly growing. Currently there is no standardized method to determine the dynamic range of scanners. Therefore the data reported in technical specifications can be determined using different methods. An ISO 21550 Standard to measure the ability of scanners to reproduce tones especially in the dark areas of the original is currently under development (in an early working draft stage). At the present time most of the manufacturers report the dynamic range calculated from the bit depth of the implemented A/D conversion using the formula

Towards Optimal Indexing for Segment Databases

. Segment databases store N non-crossing but possibly touching segments in secondary storage. Efficient data structures have been proposed to determine all segments intersecting a vertical line (stabbing queries). In this paper, we consider a more general type of query for segment databases, determining intersections with respect to a generalized segment (a line, a ray, a segment) with a fixed angular coefficient. We propose two solutions to solve this problem. The first solution has optimal O( N B ) space complexity, where N is the database size and B is the page size, but the query time is far from optimal. The second solution requires O( N B log 2 B) space, the query time is O(log B N B (log B N B +log 2 B+ IL (B)) + T B ), which is very close to the optimal, and insertion amortized time is O(log B N B + log 2 B + 1 B log 2 B N B ), where T is the size of the query result, and IL (B) is a small constant, representing the number of times we must repeatedly apply the log..