Ian Parberry

Parallel Computation with Threshold Functions

We study two classes of unbounded fan-in parallel computation, the standard one, based on unbounded fan-in ANDs and ORs, and a new class based on unbounded fan-in threshold functions. The latter is motivated by a connectionist model of the brain used in Artificial Intelligence. We are interested in the resources of time and address complexity. Intuitively, the address complexity of a parallel machine is the number of bits needed to describe an individual piece of hardware. We demonstrate that (for WRAMs and uniform unbounded fan-in circuits) parallel time and address complexity is simultaneously equivalent to alternations and time on an alternating Turing machine (the former to within a constant multiple, and the latter a polynomial). In particular, for constant parallel time, the latter equivalence holds to within a constant multiple. Thus, for example, polynomial-processor, constant-time WRAMs recognize exactly the languages in the logarithmic time hierarchy, and polynomial-word-size, constant-time WRAMs recognize exactly the languages in the polynomial time hierarchy. As a corollary, we provide improved simulations of deterministic Turing machines by constant-time shared-memory machines. Furthermore, in the threshold model, the same results hold if we replace the alternating Turing machine with the analogous threshold Turing machine, and replace the resource of alternations with the corresponding resource of thresholds. Threshold parallel computers are much more powerful than the standard models (for example, with only polynomially many processors, they can compute the parity function and sort in constant time, and multiply two integers in O(log*n) time), and appear less amenable to known lower-bound proof techniques.

Optimal Path Planning for Mobile Robot Navigation

Some optimal path planning algorithms for navigating mobile rectangular robot among obstacles and weighted regions are presented. The approach is based on a higher geometry maze routing algorithm. Starting from a top view of a workspace with obstacles, the so-called free workspace is first obtained by virtually expanding the obstacles in the image. After that, an 8-geomerty maze routing algorithm is applied to obtain an optimal collision-free path with linear time and space complexities. The proposed methods cannot only search an optimal path among various terrains but also find an optimal path for the 2-D piano movers problem with 3 DOF. Furthermore, the algorithm can be easily extended to the dynamic collision avoidance problem among multiple autonomous robots or path planning in the 3-D space.

On the construction of parallel computers from various bases of Boolean functions

The effects of bases of two-input boolean functions are characterised in terms of their impact on some questions in parallel computation. It is found that a certain set of bases (called the P-complete set) which are not necessarily complete in the classical sense, apparently makes the circuit value problem difficult, and renders extended Turing machines and conglomerates equal to general parallel computers. A class of problems called EP arises naturally from this study, relating to the parity of the number of solutions to a problem, in contrast to previously defined classes concerning the count of the number of solutions (#P) or the existence of solutions to a problem (NP). Tournament isomorphism is a member of EP.

Experience with an industry-driven capstone course on game programming: extended abstract

Game programming classes have been offered at the University of North Texas continuously since 1993. The classes are project based, and feature collaborative coursework with art majors in UNTs School of Visual Arts. We discuss the design that enables them to simultaneously provide both training for students intending employment in the game industry, and a capstone experience for general computer science undergraduates.

Controlled Procedural Terrain Generation Using Software Agents

Procedural terrain generation is used to create landforms for applications such as computer games and flight simulators. While most of the existing work has concentrated on algorithms that generate terrain without input from the user, we explore a more controllable system that uses intelligent agents to generate terrain elevation heightmaps according to designer-defined constraints. This allows the designer to create procedural terrain that has specific properties.

The art and science of game programming

The University of North Texas has for many years offered classes in game programming to Computer Science students and classes in game art and design to art students. A key feature of these classes is the opportunity for these diverse communities of students to collaborate on joint projects. We describe the features that make these classes unique.

An efficient algorithm for the knight's tour problem

A knight’s tour is a series of moves made by a knight visiting every square of an n x n chessboard exactly once. The knight’s tour problem is the problem of constructing such a tour, given n. A knight’s tour is called closed if the last square visited is also reachable from the first square by a knight’s move, and open otherwise. Define the knight’s graph for an n x n chessboard to be the graph G = (V,E), where V={(i,j) ( 1 d i,j Gn}, and E={((i,j),(k,Q) ( {Ii-kl,Ijt[} = {1,2}}. That is, there is a vertex for every square of the board and an edge between two vertices exactly when there is a knight’s move from one to the other. Then, more formally, an open knight’s tour is defined to be a Hamiltonian path, and a closed knight’s tour is defined to be a Hamiltonian cycle on a knight’s graph. A knight’s graph has n2 vertices and 4n2 12n + 8 edges. The formal study of the knight’s tour problem is said to have begun with Euler [lo] in 1759, who considered the standard 8 x 8 chessboard. Rouse Ball and Coxeter [l] give an interesting bibliography of the history of the problem from this point. Dudeney [8, 91 contains a description of exactly which rectangular chessboards have knight’s tours; in particular, an n x n chessboard has a closed knight’s tour iff n Z 6 is even, ’ and an open knight’s tour iff n 3 5. It is not clear who first proved this fact, but it appears to be part of the folklore of the subject (see, for example, [2]). There exist several independently conceived linear time (i.e. O(n2)) algorithms for constructing knight’s tours (see, for example, [5, 191). Takemji and Lee [22, 231 recently proposed a neural network solution to the knight’s tour problem, although it appears to be of little use in practice (see [ 17, 181). We will describe in this paper a new, simple, and fast algorithm for constructing knight’s tours on square boards.

A real-time algorithm for the (n 2 − 1)-puzzle

Abstract A real-time algorithm for the (n2 − 1)-puzzle is designed using greedy and divide-and-conquer techniques. It is proved that (ignoring lower order terms) the new algorithm uses at most 5n3 moves, and that any such algorithm must make at least n3 moves in the worst case, at least 2n 3 3 moves on average, and with probability one, at least 0.264n3 moves on random configurations.

A method for searching optimal routes with collision avoidance on raster charts

Collision avoidance is an intensive discussion issue for navigation safety. This article introduces a new routing algorithm for finding optimal routes with collision detection and avoidance on raster charts or planes. After the required data structure of the raster chart is initialized, the maze routing algorithm is applied to obtain the particular route of each ship. Those ships that have potential to collide will be detected by simulating the particular routes with ship domains. The collision avoidance scheme can be achieved by using the collision-area-marking method with collision avoidance rules at sea. The algorithm has linear time and space complexities, and is sufficiently fast to perform real-time routing on the raster charts.

Digital gaming as a vehicle for learning

1. Summary During the past two years there has been a resurgence of interest in how to use digital games (e.g. video games, computer games and simulations) to support instruction in a variety of fields[3,9]. The focus is on how to exploit the rich interactivity of 3-D, multiplayer virtual worlds. Computer science education has, for the most part, taken a different approach: rather than having our students play video games to learn concepts we ask them to build games to learn concepts [2,5,6,7,8]. In the process of building games, students become immersed in gaming. Yet neither the IEEE/ACM CC2001 [1] curricular recommendations, nor the ABET/CAC [4] criteria mention the notion of gaming. This panel addresses the still controversial question of whether gaming is a legitimate component of computing, and if so, where does it fit within the curriculum. Regardless of where or how gaming falls within the curriculum, it is touted as an approach that will be attractive to a diverse audience, thus increasing potential enrollment into more traditional computer science courses. However, implementing a fully robust, modern, visually compelling, multi-player game from scratch as a semester-long project is problematic. The members of this panel will share a range of experiences in how to exploit a game format to meet particular pedagogic goals. The holy grail of modern commercial game design remains the “First Person Shooter,” (FPS) a game in which a character views a 3-D world from a first person, rather than map or textbased perspective, and with weapon (gun) in hand, moves through an interactive story to attain some goal. Typically there is a lot of shooting and consequent blood and guts. The genre, despite its violent roots, supports some of the most sophisticated techniques of computer graphics, animation and visualization. FPS open source game engines also provide compelling vehicles through which to teach good software design including design approaches for agent-based artificial intelligence and peer-to-peer networks. As a group we will each present our views on this controversy and suggest ways in which FPS can leave its violent roots in a manner similar to how the “kill text” button in early text editors became a more benign “cut” or “copy.” There appear to be four approaches to incorporating digital gaming into CS curriculum: (1) to support foundations courses, e.g. CS 1, (2) to provide specialized content at the upper level to prepare students for the gaming and animation industry, (3) to provide a curriculum encompassing thematic approach to CS in order to make CS and game development accessible to a more diverse population, (4) to provide trans-disciplinary experiences for CS students where they learn to interact with experts from other disciplines. A unique aspect of this panel is that all of us have had experience of some sort with all of these approaches. Consequently, the names attached to the sections below reflect a somewhat arbitrary assignment by the moderator. Like any good game, each of us will assume a role and run with it, supporting our assigned character. The format of the session will consists of a brief overview, a short presentation of each approach, a set of challenges to the audience, and hopefully, a lively interactive discussion of the place of gaming in the curriculum.