concerning the computational complexity for packet scheduling algorithms to achieve tight end-to-end delay bounds. We rst focus on the dierence between the time a packet nishes service in a scheduling algorithm and its virtual nish time under a GPS (General Processor Sharing) scheduler, called GPS-relative delay. We prove that, under a slightly restrictive but reasonable computational model, the lower bound computational complexity of any scheduling algorithm that guarantees O(1) GPS-relative delay bound is log2n) (widely believed as a \folklore theorem" but never proved). We also discover that, surprisingly, the complexity lower bound remains the same even if the delay bound is relaxed to O(n ) for 0 < a < 1. This implies that the delaycomplexity tradeo curve is \at" in the \interval" [O(1), O(n)). We later extend both complexity results (for O(1) ) delay) to a much stronger computational model. Finally, we show that the same complexity lower bounds are conditionally applicable to guaranteeing tight end-to-end delay bounds. This is done by untangling the relationship between the GPS-relative delay bound and the end-to-end delay bound.

We offer a preliminary report on a research program to investigate versatile algorithms for document image content extraction, that is locating regions containing handwriting, machine-print text, graphics, line-art, logos, photographs, noise, etc. To solve this problem in its full generality requires coping with a vast diversity of document and image types. Automatically trainable methods are highly desirable, as well as extremely high speed in order to process large collections. Significant obstacles include the expense of preparing correctly labeled (“ground-truthed”) samples, unresolved methodological questions in specifying the domain (e.g. what is a representative collection of document images?), and a lack of consensus among researchers on how to evaluate content-extraction performance. Our research strategy emphasizes versatility first: that is, we concentrate at the outset on designing methods that promise to work across the broadest possible range of cases. This strategy has several important implications: the classifiers must be trainable in reasonable time on vast data sets; and expensive ground-truthed data sets must be complemented by amplification using generative models. These and other design and architectural issues are discussed. We propose a trainable classification methodology that marries k-d trees and hash-driven table lookup and describe preliminary experiments.

This paper is concerned with the problem of computing spanning tree (MST) for n points in a p-dimensional space where the "distance" between each pair of points i and j satisfies the relationship' dq max {Ixti - xtql} , where xki is the coordinate of object i along the ktti dimension. This relationship is clearly satisfied by all Minkowski metrics dq = [ Ixki - xnjl r] x/r, r > 1

. Clustering is an important data exploration task. A prominent clustering algorithm is agglomerative hierarchical clustering. Roughly, in each iteration, it merges the closest pair of clusters. It was first proposed way back in 1951, and since then there have been numerous modifications. Some of its good features are: a natural, simple, and nonparametric grouping of similar objects which is capable of finding clusters of different shape such as spherical and arbitrary. But large CPU time and high memory requirement limit its use for large data. In this paper we show that geometric metric (centroid, median, and minimum variance) algorithms obey a 90-10 relationship where roughly the first 90iterations are spent on merging clusters with distance less than 10the maximum merging distance. This characteristic is exploited by partially overlapping partitioning. It is shown with experiments and analyses that different types of existing algorithms benefit excellently by drastical...

For a sample of points drawn uniformly from either the d-dimensional torus or the d-cube, d 2, we give limiting distributions for the largest of the nearest-neighbor links. For d- 3 the behavior in the torus is proved to be different from the behavior in the cube. The results given also settle a conjecture of Henze (1982) and throw light on the choice of the cube or torus in some probabilistic models of computational complexity of geometrical al-gorithms.