John L. Pfaltz

Distance functions on digital pictures

Abstract This paper describes algorithms for computing various functions on a digital picture which depend on the distance to a given subset of the picture. The algorithms involve local operations which are performed repeatedly, “in parallel”, on every picture element and its immediate neighbors. Applications to the detection of “clusters” and “regularities” in a picture, and to the dissection of a region into “pieces”, are also described.

Partial-match retrieval using indexed descriptor files

In this paper we describe a practical method of partial-match retrieval in very large data files. A binary code word, called a descriptor, is associated with each record of the file. These record descriptors are then used to form a derived descriptor for a block of several records, which will serve as an index for the block as a whole; hence, the name “indexed descriptor files.” First the structure of these files is described and a simple, efficient retrieval algorithm is presented. Then its expected behavior, in terms of storage accesses, is analyzed in detail. Two different file creation procedures are sketched, and a number of ways in which the file organization can be “tuned” to a particular application are suggested.

Web grammars and picture description

This paper describes an investigation of the practicality of describing pictures using linguistic structures other than strings-in particular, using labelled directed graphs (“webs”). A parsing program for a class of “neural network” pictures is demonstrated.

Summary of the final report of the NSF workshop on scientific database management

The National Science Foundation sponsored a two day workshop hosted by the University of Virginia on March 12-13, 1990 at which representatives from the earth, life, and space sciences met with computer scientists to discuss the issues facing the scientific community in the area of database management. The workshop1 participants concluded that initiatives by the National Science Foundation and other funding agencies, as well as specific discipline professional societies are urgently needed to address the problems facing scientists with respect to data management. This article presents a condensed version of the workshop final report emphasizing the technical research issues.

Convexity in directed graphs

Abstract In this paper the concept of convexity in directed graphs is described. It is shown that the set of convex subgraphs of a directed graph G partially ordered by inclusion forms a complete, semimodular, A-regular lattice, denoted ℒG. The lattice theoretic properties of the convex subgraph lattice lead to inferences about the path structure of the original graph G. In particular, a graph factorization theorem is developed. In Section 4, several graph homomorphism concepts are investigated in relation to the preservation of convexity properties. Finally we characterize an interesting class of locally convex directed graphs.

Closure spaces that are not uniquely generated

Because antimatroid closure spaces satisfy the anti-exchange axiom, it is easy to show that they are uniquely generated. That is, the minimal set of elements determining a closed set is unique. A prime example is a discrete convex geometry in Euclidean space where closed sets are uniquely generated by their extreme points. But, many of the geometries arising in computer science, e.g. the world wide web or rectilinear VLSI layouts are not uniquely generated. Nevertheless, these closure spaces still illustrate a number of fundamental antimatroid properties which we demonstrate in this paper. In particular, we examine both a pseudo-convexity operator and the Galois closure of formal concept analysis. In the latter case, we show how these principles can be used to automatically convert a formal concept lattice into a system of implications.

Closure systems and their structure

Abstract Closure is a fundamental property of many discrete systems. Transitive closure in relations has been well studied, as has geometric convexity closure and closure in various kinds of graphs. The closed sets of these uniquely generated, antimatroid operators illustrate a well-behaved internal structure. This paper shows that much of this structure is preserved by even closure operators that are not uniquely generated.

Graph Structures

The concept of a graph structure So in which a tree-like assemblage of subgraphs is used to represent a directed graph G is developed. This is directly analogous to the representation of lists by list structures. It is shown that with suitable restrictions, given So , G can be uniquely determined, and conversely, given G, So can be effectively constructed. A computer implementation which minimizes storage to represent G is presented, together with algorithms that illustrate the utility of graph structures, in particular, one that efficiently determines the existence of paths in G.

Scalable, parallel, scientific databases

Large scientific applications which rely on highly parallel computational analysis require highly parallel data access. We describe an object-oriented scientific database system that achieves nearly linear scale-up over large, million object data sets. Of primary importance are those features which seem central to the development of this, or any other parallel database system. These include techniques of object distribution, of multi-operator parallelism, and of indirect object referencing. It also appears to require a query server architecture instead of the more common page server configurations.

Mathematical continuity in dynamic social networks

A rigorous concept of continuity for dynamic networks is developed. It is based on closed, rather than open, sets. It is local in nature, in that if the network change is discontinuous it will be so at a single point and the discontinuity will be apparent in that point’s immediate neighborhood. Necessary and sufficient criteria for continuity are provided when the change involves only the addition or deletion of individual nodes or connections (edges). Finally, we show that an effective network process to reduce large networks to their fundamental cycles is continuous.