We propose to extend database systems by a Skyline operation. This operation filters out a set of interesting points from a potentially large set of data points. A point is interesting if it is not dominated by any other point. For example, a hotel might be interesting for somebody traveling to Nassau if no other hotel is both cheaper and closer to the beach. We show how SSL can be extended to pose Skyline queries, present and evaluate alternative algorithms to implement the Skyline operation, and show how this operation can be combined with other database operations, e.g., join.

The Skyline operator

f High-performance, special-purpose computer systems are typically used to meet specific application requirements or to off-load computations that are especially taxing to general-purpose computers. As hardware cost and size continue to drop and processing requirements become well-understood in areas such as signal and image processing, more special-purpose systems are being constructed. However, since most of these systems are built on an ad hoc basis for specific tasks, methodological work in this area is rare. Because the knowledge gaited from individual experiences is neither accumulated nor properly organized, the same errors are repeated. I/O and computation imbalance is a notable example-often, the fact that I/O interfaces cannot keep up with device speed is discovered only after constructing a high-speed, special-purpose device. We intend to help correct this ad hoc approach by providing a general guideline-specifically, the concept of systolic architecture, a general methodology for mapping high-level computations into hardware structures. In a systolic system, data flows from the computer memcory in a rhythmic fashion, passing through many processing elements before it returns to memory, much as blood circulates to and from the heart. The system works like an autombbile assembly line where different people work on the same car at different times and many cars are assembled simultaneously. An assembly line is always linear, however, and systolic systems are sometimes two-dimensional. They can be rectangular, triangular, or hexagonal to make use of higher degrees of parallelism. Moreover, to implement a variety of computations, data flow in a systolic system may be at multiple speeds in multiple directions-both inputs and (partial) results flow, whereas only results flow in classical pipelined systems. Generally speaking, a systolic system is easy to implement because of its regularity and easy to reconfigure (to meet various outside constraints) because of its modularity. The systolic architectural concept was developed at Carnegie-Mellon University,'17 and versions of systolic processors are being designed and built by several industrial and governmental organizations.840 This article reviews the basic principle of systolic architectures and explains why they should result in cost-effective, highperformance special-purpose systems for a wide range of problems.

/pdf/why-systolic-architectures-27b11gsxcr.pdf

Why systolic architectures

An interconnection pattern of processing elements, the cube-connected cycles (CCC), is introduced which can be used as a general purpose parallel processor. Because its design complies with present technological constraints, the CCC can also be used in the layout of many specialized large scale integrated circuits (VLSI). By combining the principles of parallelism and pipelining, the CCC can emulate the cube-connected machine and the shuffle-exchange network with no significant degradation of performance but with a more compact structure. We describe in detail how to program the CCC for efficiently solving a large class of problems that include Fast Fourier transform, sorting, permutations, and derived algorithms.

/pdf/the-cube-connected-cycles-a-versatile-network-for-parallel-4wi8zf52ph.pdf

The cube-connected cycles: a versatile network for parallel computation

This book introduces a new approach to the design and implementation of software systems which will help users of large scale parallel systems coordinate many concurrent activities toward a single goal It assesses the strengths an weaknesses of this approach with existing alternativesCole's system proposes a selection of independent algorithmic skeletons, each of which describes the structure of a particular style of algorithm The user must describe a solution to a problem as an instance of the appropriate skeleton The implementation task is simplified by the fact that each skeleton may be considered independently, in contrast to the monolithic programming interfaces of existing systems at a similar level of abstractionThe book describes four skeletons based on the notions of fixed degree divide and conquer, task queues, iterative combination, and clustering Each is introduced in terms of the abstraction it presents to the user Implementation on a square grid of autonomous processor memory pairs is considered and examples of problems which could be solved in terms of the skeleton are presentedMurray I Cole is a Lecturer in the Computing Science Department of the University of Glasgow "Algorithmic Skeletons" is included in the series Research Monographs in Parallel and Distributed Computing, Copublished with Pitman Publishing,

/pdf/algorithmic-skeletons-structured-management-of-parallel-2u29jsqtry.pdf

Algorithmic skeletons : structured management of parallel computation

Skyline queries ask for a set of interesting points from a potentially large set of data points. If we are traveling, for instance, a restaurant might be interesting if there is no other restaurant which is nearer, cheaper, and has better food. Skyline queries retrieve all such interesting restaurants so that the user can choose the most promising one. In this paper, we present a new online algorithm that computes the Skyline. Unlike most existing algorithms that compute the Skyline in a batch, this algorithm returns the first results immediately, produces more and more results continuously, and allows the user to give preferences during the running time of the algorithm so that the user can control what kind of results are produced next (e.g., rather cheap or rather near restaurants).

/pdf/shooting-stars-in-the-sky-an-online-algorithm-for-skyline-4rx1em92uh.pdf

Shooting stars in the sky: an online algorithm for skyline queries

Two algorithms are presented for sorting n2 elements on an n × n mesh-connected processor array that require O (n) routing and comparison steps. The best previous algoritmhm takes time O(n log n). The algorithms of this paper are shown to be optimal in time within small constant factors. Extensions to higher-dimensional arrays are also given.

https://dl.acm.org/doi/pdf/10.1145/359461.359481

Sorting on a mesh-connected parallel computer

A maximal vector of a set ~s one which is not less than any other vector m all components We derive a recurrence relation for computing the average number of maxunal vectors m a set of n vectors m d-space under the assumpUon that all (nl) a relative ordermgs are equally probable. Solving the recurrence shows that the average number of maxmaa is O((ln n) a-~) for fixed d We use this result to construct an algorithm for finding all the maxima that have expected running tmae hnear m n (for sets of vectors drawn under our assumptions) We then use the result to find an upper bound on the expected number of convex hull points m a random point set

/pdf/on-the-average-number-of-maxima-in-a-set-of-vectors-and-4e6jmwbqtf.pdf

On the Average Number of Maxima in a Set of Vectors and Applications

We present new algorithms for dynamic programming and transtivc closure which arc appropriate
for very large-scale integration implementation.

Direct VLSI Implementation of Combinatorial Algorithms

Two algorithms for sorting n2 elements on an n×n mesh-connected processor array that require 0(n) routing and comparison steps are presented. The best previous algorithms take time 0(n log n). Our algorithms are shown to be optimal in time within small constant factors.

C. D. Thompson

Papers

Sorting on a mesh-connected parallel computer

On the Average Number of Maxima in a Set of Vectors and Applications

Direct VLSI Implementation of Combinatorial Algorithms

Sorting on a mesh-connected parallel computer