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The nearest neighbor searching problem (also called the post office problem) calls for organizing the set P of N points in k-space so that the nearest neighbor in P to a new point can be quickly found. Friedman, Baskett and Shustek describe an algorithm for nearest neighbor searching based on projecting the points onto the various coordinate axes; their analysis of this method shows that a nearest...
Algorithms that manipulate sets of rectangles are of rectangles are of great practical importance in VLST design systems and other applications. Although much theoretical work has appeared recently on the complexity of rectangle problems, it has assumed that the inputs are given as a list of rectangles. In this paper we study the complexity of rectangle problems when the inputs are given in a hierarchical...
Kung [1979b] has recently enunciated a set of principles for designing algorithms for implementation in Very Large Scale Integrated circuitry (VLSI), and supported these principles by displaying a number of particular algorithms based on various "communication geometries". In this paper we will examine a communication geometry which Kung calls the "one-dimensional array of processors",...
In this paper we study a class of resource tradeoffs that arise in such problems as parallel sorting algorithms, linear recursion schemata, VLSI layouts, and searching problems. The tradeoffs can all be traced to the common structure of a multiway tree, and the special class of binomial trees (which are isomorphic to the binomial coefficients) correspond to particularly efficient algorithms. Although...
In this paper we will investigate transformations that serve as tools in the design of new data structures. Specifically, we study general methods for converting static structures (in which all elements are known before any searches are performed) to dynamic structures (in which the insertion of a new element can be mixed with searches). We will see three classes of such transformations (each based...
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