Paul S. LaFollette

Loopless generation of Gray codes for k -ary trees

A number of loopless binary and k-ary tree generation algorithms are known. Vajnovszki recently presented a loopless Gray code generation algorithm for binary trees based on rotations and variations. He used a representation introduced by Pallo and generated the Gray code of Roelants van Baronaigien and Ruskey. In this paper we generalize the representation to k-ary trees and base the loopless generation algorithm on the shifts of Korsh and Lipschutz.

A system for program visualization in the classroom

This paper describes the use of a system which will allow effortless visualization and animation of standard C/C++ programs. The system brings alive programs so that students in CS 1 and CS 2 classes can more easily see each instruction and its effects. They can also see the effects of larger entities such as functions. The system serves as an excellent instructional tool and debugger.

A Visual Interface for Effortless Animation of C/C++ Programs

This paper introduces a software visualization system that (i) creates animations of programs without the programmer writing any animation code, and (ii) provides a window interface that automatically displays program information, explicitly showing the scope and context of its data, and allowing considerable control over animation displays. Programs are specified in textual form but the system creates high-level dynamic displays using bit-mapped graphics and window-interface technology. The dynamics of the displays make a program come to life. The current system was designed primarily for use in CS-I and CS-II courses. Therefore, it assumes that programs will use acyclic linked data structures and relatively small data sets. It provides the programmer no control over the animations and only limited control over the layout. However, we feel this is a reasonable trade-off for the ease of use the system provides.

Geometric and intensity distortion in echography

Anatomic structures possessing varying sonic propagation velocities refract ultrasonic beams and create distortions in the sonographic image. The distortions consist of inaccurate positioning of echogenic locations (geometric distortions) and of inaccurate display of ultrasonic intensities (intensity distortions). Artifacts of both types occur in the region distal to a structure of circular cross section with an internal sonic propagation velocity lower than that of its surroundings. In an attempt to better understand these distortions, a model is developed from first principles of the production of sonograms of such a region. Assuming a uniform ultrasonic beam and uniform echogenicity of the surrounding tissue, a mathematical expression has been derived for the intensity of the sound arriving at each point and returning to the transducer. Computer simulations of the resulting sonographic image are provided for visualization. In spite of many simplifying assumptions, this model is shown to be consistent with several known artifacts, and provides insight into the mechanisms of their production.

Effect of scan format on refraction artifacts

Refraction artifacts occur when the ultrasound beam is bent from its original direction as it passes through a boundary between tissues having different sound speeds. Refraction artifacts result in both the improper positioning and the improper brightness of echoes displayed in clinical sonograms. The effect of scan format on the sonographic appearance of several refraction artifacts due to a circular object possessing a sonic speed differing from its surrounding tissue was studied using a mathematical model and computer generated images. A quantitative index of artifact prominence was developed to compare the differences between the rectilinear and the sector scan formats. Theoretically predicted results were compared with actual sonograms of a specially designed phantom. Results included the finding that the retrolenticular afterglow was more prominent in the sector scan format, and that differences were most prominent when the refracting object was close to the transducer.

A loopless Gray code for rooted trees

Beyer and Hedetniemi [1980] gave the first constant average-time algorithm for the generation of all rooted trees with n nodes. This article presents the first combinatorial Gray code for these trees and a loopless algorithm for its generation.

Constant time generation of derangements

This paper presents the first constant time generation algorithm for derangements--permutations with no fixed points. Each derangement is obtained from its predecessor by making either one transposition or one rotation of three elements. It also generalizes this to permutations with a bounded number of fixed points.

Multiset Permutations and Loopless Generation of Ordered Trees with Specified Degree Sequence

An ordered tree with specified degree sequence and n internal nodes has ai nodes of degree i, where a0=1+?i=1(i?1)ai and n=?i=0ai. This paper presents the first loopless algorithm for generating all ordered trees with specified degree sequence. It uses a new version of the algorithm for generating multiset permutations. When ak=N, a0=(k?1)N+1, and all other ais are 0, all N node k-ary trees are generated.

Loopless Generation of Linear Extensions of a Poset

Canfield and Williamson gave the first loopless algorithm for generating all linear extensions of a poset. It elegantly generates all signed extensions, resulting in each extension appearing somewhere with each sign, but retains only every other one independent of its sign. It uses an array for the extension. In this paper we give another loopless algorithm for generating all the linear extensions. It generates each extension only once and uses a list for the extensions.

Loopless Generation of Schröder Trees

The well-known Schröder numbers have appeared in different combinatorial contexts, including Schröder trees and well-weighted binary trees. The only loopless algorithm for generating Schröder trees actually generated representations for their well-weighted binary tree counterparts. This paper presents the first loopless algorithms for directly generating Schröder tree representations. They use a new loopless algorithm for generating k-compositions of n in inverse lexicographic order.