Showing papers by "Alejandro López-Ortiz published in 2000"

Adaptive set intersections, unions, and differences

Abstract: Motivated by boolean queries in text database systems, we consider the problems of finding the intersection, union, or difference of a collection of sorted sets. While the worst-case complexity of these problems is straightforward , we consider a notion of complexity that depends on the particular instance. We develop the idea of a proof that a given set is indeed the correct answer. Proofs, and in particular shortest proofs, are characterized. We present adaptive algorithms that make no a priori assumptions about the problem instance, and show that their running times are within a constant factor of optimal with respect to a natural measure of the difficulty of an instance. In the process, we develop a framework for designing and evaluating adaptive algorithms in the comparison model. 1 Introduction and Overview Our work can be seen in the general context of performing searches quickly in a database or data warehousing environment. The broad issue is that of characterizing what type of join operations can be performed without scanning the relations involved or actually materializing intermediate relations. The specific problem addressed here can be seen in that context or in the context of performing a web search, or a search in another large text database, for documents containing some or all of a set of keywords. For each keyword we are given the set of references to documents in which it occurs [2, 6, 9]. These sets are stored in some natural order, such as document date. In practice, the sets are large. For example, the average word from user query logs matches approximately a million documents on the AltaVista web search engine. Of course, one would hope that the answer to the query is small, particularly if the query is an intersection. It may also be expected that the elements of such an intersection are not spread uniformly through the initial

Online Routing in Convex Subdivisions

Abstract: We consider online routing algorithms for finding paths between the vertices of plane graphs. We show (1) there exists a routing algorithm for arbitrary triangulations that has no memory and uses no randomization, (2) no equivalent result is possible for convex subdivisions, (3) there is no competitive online routing algorithm under the Euclidean distance metric in arbitrary triangulations, and (4) there is no competitive online routing algorithm under the link distance metric even when the input graph is restricted to be a Delaunay, greedy, or minimum-weight triangulation.