Martin Henz

Global constraints for round robin tournament scheduling

Abstract In the presence of side-constraints and optimization criteria, round robin tournament problems are hard combinatorial problems, commonly tackled with tree search and branch-and-bound optimization. Recent results indicate that constraint-based tree search has crucial advantages over integer programming-based tree search for this problem domain by exploiting global constraint propagation algorithms during search. In this paper, we analyze arc-consistent propagation algorithms for the global constraints “all-different” and “one-factor” in the domain of round robin tournaments. The best propagation algorithms allow us to compute all feasible perfectly mirrored pattern sets with minimal breaks for intermural tournaments of realistic size, and to improve known lower bounds for intramural tournaments balanced with respect to carry-over effects.

Scheduling a Major College Basketball Conference--Revisited

Nemhauser and Trick presented the problem of finding a timetable for the 1997/1998 Atlantic Coast Conference (ACC) in basketball. Their solution, found with a combination of integer programming and exhaustive enumeration, was accepted by the ACC.Finite-domain constraint programming is another programming technique that can be used for solving combinatorial search problems such as sports tournament scheduling. This paper presents a solution of round-robin tournament planning based on finite-domain constraint programming. The approach yields a dramatic performance improvement, which makes an integrated interactive software solution feasible.

Using Oz for College Timetabling

In this paper, we concentrate on a typical scheduling problem: the computation of a timetable for a German college. Like many other scheduling problems, this problem contains a variety of complex constraints and necessitates special-purpose search strategies. Techniques from Operations Research and traditional constraint logic programming are not able to express these constraints and search strategies on a sufficiently high level of abstraction. We show that the higher-order concurrent constraint language Oz provides this high-level expressivity, and can serve as a useful programming tool for college timetabling.

COMPOzE-intention-based music composition through constraint programming

We goal of the work is to derive four-voice music pieces from given musical plans, which describe the harmonic flow and the intentions of a desired composition. We developed the experimentation platform COMPOzE for intention based composition. COMPOzE is based on constraint programming over finite domains of integers. We argue that constraint programming provides a suitable technology for this task and that the libraries and tools available for the constraint programming system Oz effectively support the implementation of COMPOzE. This work links the research areas of automatic music composition on one hand and finite domain constraint programming on the other, and contributes the tool COMPOzE, which practically demonstrates the potential of constraint programming to open up new areas of application for automatic music composition.

Objects in Oz

The programming language Oz integrates the paradigms of imperative, functional and concurrent constraint programming in a computational framework of unprecedented breadth, featuring stateful programming through cells, lexically scoped higher-order programming, and explicit concurrency synchronized by logic variables. Object-oriented programming is another paradigm that provides a set of concepts useful in software practice. In this thesis we address the question how object-oriented programming can be suitably supported in Oz. As a lexically scoped higher-order language, Oz can express a wide range of object-oriented concepts. We present a simple yet expressive object system, demonstrate its usability and outline an efficient implementation. A central aspect of Oz is its support for concurrent computation. We examine the impact of concurrency on the design of an object system and explore the use of objects in concurrent programming.

SudokuSat—A Tool for Analyzing Difficult Sudoku Puzzles

Sudoku puzzles enjoy world-wide popularity, and a large community of puzzlers is hoping for ever more difficult puzzles. A crucial step for generating difficult Sudoku puzzles is the fast assessment of the difficulty of a puzzle. In a study in 2006, it has been shown that SAT solving provides a way to efficiently differentiate between Sudoku puzzles according to their difficulty, by analyzing which resolution technique solves a given puzzle. This paper shows that one of these techniques—unit resolution with failed literal propagation—does not solve a recently published Sudoku puzzle called AI Escargot, claimed to be the world’s most difficult. The technique is also unable to solve any of a list of difficult puzzles published after AI Escargot, whereas it solves all previously studied Sudoku puzzles. We show that the technique can serve as an efficient and reliable computational method for distinguishing the most difficult Sudoku puzzles. As a proof-of-concept for an efficient difficulty checker, we present the tool SudokuSat that categorizes Sudoku puzzles with respect to the resolution technique required for solving them.

A Toolkit for Constraint-Based Inference Engines

Solutions to combinatorial search problems can benefit from custom-made constraint-based inference engines that go beyond depth-first search. Several constraint programming systems support the programming of such inference engines through programming abstractions. For example, the Mozart system for Oz comes with several engines, extended in dimensions such as interaction, visualization, and optimization. However, so far such extensions are monolithic in their software design, not catering for systematic reuse of components. We present an object-oriented modular architecture for building inference engines that achieves high reusability and supports rapid prototyping of search algorithms and their extensions. For the sake of clarity, we present the architecture in the setting of a C++ constraint programming library. The SearchToolKit, a search library for Oz based on the presented architecture, provides evidence for the practicality of the design.

Hardware Implementations of Real-Time Reconfigurable WSAT Variants

Local search methods such as WSAT have proven to be successful for solving SAT problems. In this paper, we propose two host-FPGA (Field Programmable Gate Array) co-implementations, which use modified WSAT algorithms to solve SAT problems. Our implementations are reconfigurable in real-time for different problem instances. On an XCV1000 FPGA chip, SAT problems up to 100 variables and 220 clauses can be solved. The first implementation is based on a random strategy and achieves one flip per clock cycle through the use of pipelining. The second uses a greedy heuristic at the expense of FPGA space consumption, which precludes pipelining. Both of the two implementations avoid re-synthesis, placement, routing for different SAT problems, and show improved performance over previously published reconfigurable SAT implementations on FPGAs.

Teaching experience: logic and formal methods with coq

During the past three years we have been integrating mechanized theorem proving into a traditional introductory course on formal methods. We explain our goals for adding mechanized provers to the course, and illustrate how we have integrated the provers into our syllabus to meet those goals. We also document some of the teaching materials we have developed for the course to date, and what our experiences have been like.

Automated Generation of Geometry Questions for High School Mathematics

We describe a framework that combines a combinatorial approach, pattern matching and automated deduction to generate and solve geometry problems for high school mathematics. Such a system would help teachers to quickly generate large numbers of questions on a geometry topic. Students can explore and revise specific topics covered in classes and textbooks based on generated questions. The system can act as a personalized instructor - it can generate problems that meet users specific weaknesses. This system may also help standardize tests such as GMAT and SAT. Our novel methodology uses (i) a combinatorial approach for generating geometric figures (ii) a pattern matching approach for generating questions and (iii) automated deduction to generate new questions and solutions. By combining these methods, we are able to generate questions involving finding or proving relationships between geometric objects based on a specification of the geometry objects, concepts and theorems to be covered by the questions. Experimental results show that a large number of questions can be generated in a short time. We have tested our generated questions on an existing geometry question solving software JGEX, verifying the validity of the generated questions.