Large-Scale Sorting in Uniform Memory Hierarchies

We present several e cient algorithms for sorting on the uniform memory hierarchy (UMH), introduced by Alpern, Carter, and Feig, and its paral- lelization P-UMH.We give optimal and nearly-optimal algorithms for a wide range of bandwidth degradations, including a parsimonious algorithm for constant bandwidth. We also develop optimal sorting algorithms for all bandwidths for other versions of UMH and P-UMH, including natural restrictions we introduce called RUMH and P-RUMH, which more closely correspond to current programming languages

Semantic Cardinality Estimation for Queries over Objects

In this paper, we address the problem of estimating cardinalities of queries over sets of objects. We base our estimates on a knowledge of subset relationships between sets (e.g., Students form a subset of People). Previous work on cardinality estimation has assumed that every subset is a representative sample of the set it is taken from. We maintain (offline) information for the cases where the subset is not a uniform representative, and use this information to improve the accuracy of our cardinality estimates. We present cardinality estimation techniques for image sets and select sets. Image sets are created by applying a function to an existing set. Select sets contain the elements that satisfy some predicate in an existing set. Empirically we show that we can obtain estimates within a factor of four for reasonable image sets on our test database while maintaining offline statistics requiring space linear in the number of named sets in the database and the number of attributes defi..

Large-Scale Sorting in Uniform Memory Hierarchies

We present several efficient algorithms for sorting on the uniform memory hierarchy (UMH), introduced by Alpern, Carter, and Feig, and its parallelization P-UMH. We give optimal and nearly-optimal algorithms for a wide range of bandwidth degradations, including a parsimonious algorithm for constant bandwidth. We also develop optimal sorting algorithms for all bandwidths for other versions of UMH and P-UMH, including natural restrictions we introduce called RUMH and P-RUMH, which more closely correspond to current programming languages

Blocking for External Graph Searching

In this paper, we consider the problem of using disk blocks efficiently in searching graphs that are too large to fit in internal memory. Our model allows a vertex to be represented any number of times on the disk in order to take advantage of redundancy. We give matching upper and lower bounds for complete d-ary trees and d-dimensional grid graphs, as well as for classes of general graphs that intuitively speaking have a close to uniform number of neighbors around each vertex. We also show that for the special case of grid graphs blocked with isothetic hypercubes, there is a provably better speed-up if even a small amount of redundancy is permitted. Keywords: external searching, isothetic hypercubes, blocking, input/output complexity, redundancy 1 Introduction External searching is a fundamental topic in computer science and databases [1]. By "external", we mean that the records to be searched cannot fit simultaneously in the internal memory. In this paper, we consider searching in..