Christoph M. Hoffmann

Pattern Matching in Trees

ABSTgACT. Tree pattern matching is an interesting special problem which occurs as a crucial step m a number of programmmg tasks, for instance, design of interpreters for nonprocedural programming languages, automatic implementations of abstract data types, code optimization m compilers, symbohc computation, context searching in structure editors, and automatic theorem provmg. As with the sorting problem, the variations in requirements and resources for each application seem to preclude a uniform, umversal solution to the tree-pattern-matching problem. Instead, a collection of well-analyzed techmques, from which specific applications may be selected and adapted, should be sought. Five new techniques for tree pattern matching are presented, analyzed for time and space complexity, and compared with previously known methods. Particularly important are applications where the same patterns are matched against many subjects and where a subject may be modified incrementally Therefore, methods which spend some tune preprocessmg patterns in order to improve the actual matching time are included

Geometric constraint solver

Abstract The paper reports on the development of a 2D geometric constraint solver. The solver is a major component of a new generation of cad systems based on a high-level geometry representation. The solver uses a graph-reduction directed algebraic approach, and achieves interactive speed. The paper describes the architecture of the solver and its basic capabilities. Then, it discusses in detail how to extend the scope of the solver, with particular emphasis on the theoretical and human factors involved in finding a solution, in an exponentially large search space, so that the solution is appropriate to the application, and so that the way of finding it is intuitive for an untrained user.

A graph-constructive approach to solving systems of geometric constraints

A graph-constructive approach to solving systems of geometric constraints capable of effeciently handling well-constrained, overconstrained, and underconstrained configurations is presented. The geometric constraint solver works in two phases: in the analysis phase the constraint graph is analyzed and a sequence of elementary construction steps is derived, and then in the construction phase the sequence of construction steps in actually carried out. The analysis phase of the algorithm is described in detail, its correctness is proved, and an efficient algorith to realized it is presented. The scope of the graph analysis is then extended by utilizing semantic information in the form of anlge derivations, and by extending the repertoire of the construction steps. Finally, the construction phase is briefly discussed.

The problems of accuracy and robustness in geometric computation

Practical implementation of geometric operations remains error-prone, and the goal of implementing correct and robust systems for carrying out geometric computation remains elusive. The problem is variously characterized as a matter of achieving sufficient numerical precision, as a fundamental difficulty in dealing with interacting numeric and symbolic data, or as a problem of avoiding degenerate positions. The author examines these problems, surveys some of the approaches proposed, and assesses their potential for devising complete and efficient solutions. He restricts the analysis to objects with linear elements, since substantial problems already arise in this case. Three perturbation-free methods are considered: floating-point computation, limited-precision rational arithmetic, and purely symbolic representations. Some perturbation approaches are also examined, namely, representation and model, altering the symbolic data, and avoiding degeneracies.<<ETX>>

Programming with Equations

Equations provide a convenient notation for defining many computations, for example, for programming language interpreters. This paper illustrates the usefulness of equational programs, describes the problems involved in implementing equational programs, and investigates practical solutions to those problems. The goal of the study is a system to automatically transform a set of equations into an efficient program which exactly implements the logical meaning of the equations. This logical meaning may be defined in terms of the traditional mathematical interpretation of equations, without using advanced computing concepts. _

Redundant reader elimination in RFID systems

While recent technological advances have motivated large-scale deployment of RFID systems, a number of critical design issues remain unresolved. In this paper we deal with de- tecting redundant RFID readers (the redundant reader problem). The underlying difficulty associated with this problem arises from the lack of collision detection mechanisms, the potential inability of RFID readers to relay packets generated by other readers, and severe resource constraints on RFID tags. We prove that an optimal solution to the redundant reader problem is NP-hard and propose a randomized, distributed, and localized approximation algorithm, RRE. We provide a detailed probabilistic analysis of the accuracy and time complexity of RRE and conduct elaborate simulations to demonstrate their correctness and efficiency. I. INTRODUCTION

Robust set operations on polyhedral solids

An algorithm for performing regularized Boolean operation on polyhedral solids is described. Robustness is achieved by adding symbolic reasoning as a supplemental step to resolve possible numerical uncertainty. Additionally, numerical redundancy and numerical computation based on derived quantities are reduced as much as possible. Experience with an implementation of the algorithm, using a unit-cube example as a simple test object for robustness, is discussed.<<ETX>>

Generic naming in generative, constraint-based design

In generative, constraint-based design, users graphically select shape elements of design instances in order to specify shape operations that have generic intent. We discuss techniques for naming algorithmically and generically the identified geometric instance, and report on our experience with implementing these techniques. In a companion paper, we give algorithms for matching the names when editing designs.

A framework for object modeling

Abstract Modeling of products (objects) form a critical task in design and manufacturing. CAD–CAM techniques based on solid/geometric modeling have been developed for this purpose. Primarily, these methods capture the shape of the object. However, recent developments in diverse fields demand modeling schemes, which extend beyond the shape to include other relevant attributes of the object. In this paper, this issue is addressed and a new modeling framework is proposed. This framework enables the modeling of geometry and several attributes simultaneously in an integrated fashion.

On editability of feature-based design

Techniques needed for editing generative designs are presented. When a feature is edited, all features attached later must be re-evaluated to satisfy the required constraints and shape references in the initial design. We describe name matching techniques that support the design reevaluation procedure. The algorithms account for failed or multiple matches. The matching uses a naming schema based on historical, topological, and geometric design information that has been described in a companion paper.