On the reduction theory of binary forms

Cremona developed a reduction theory for binary forms of degree 3 and 4 with integer coefficients, the motivation in the case of quartics being to improve 2-descent algorithms for elliptic curves over Q. In this paper we extend some of these results to forms of higher degree. One application of this is to the study of hyperelliptic curves.

Monadic Parsing in Haskell

This paper is a tutorial on defining recursive descent parsers in Haskell. In the spirit of one-stop shopping, the paper combines material from three areas into a single source. The three areas are functional parsers, the use of monads to structure functional programs, and the use of special syntax for monadic programs in Haskell. More specifically, the paper shows how to define monadic parsers using do notation in Haskell. The paper is targeted at the level of a good undergraduate student who is familiar with Haskell, and has completed a grammars and parsing course. Some knowledge of functional parsers would be useful, but no experience with monads is assumed.

Hybrid Variable Neighborhood HyperHeuristics for Exam Timetabling Problems

This paper presents our work on analysing the high level search within a graph based hyperheuristic. The graph based hyperheuristic solves the problem at a higher level by searching through permutations of graph heuristics rather than the actual solutions. The heuristic permutations are then used to construct the solutions. Variable Neighborhood Search, Steepest Descent, Iterated Local Search and Tabu Search are compared. An analysis of their performance within the high level search space of heuristics is also carried out. Experimental results on benchmark exam timetabling problems demonstrate the simplicity and efficiency of this hyperheuristic approach. They also indicate that the choice of the high level search methodology is not crucial and the high level search should explore the heuristic search space as widely as possible within a limited searching time. This simple and general graph based hyperheuristic may be applied to a range of timetabling and optimisation problems.

Hybrid Variable Neighborhood HyperHeuristics for Exam Timetabling Problems

This paper presents our work on analysing the high level search within a graph based hyperheuristic. The graph based hyperheuristic solves the problem at a higher level by searching through permutations of graph heuristics rather than the actual solutions. The heuristic permutations are then used to construct the solutions. Variable Neighborhood Search, Steepest Descent, Iterated Local Search and Tabu Search are compared. An analysis of their performance within the high level search space of heuristics is also carried out. Experimental results on benchmark exam timetabling problems demonstrate the simplicity and efficiency of this hyperheuristic approach. They also indicate that the choice of the high level search methodology is not crucial and the high level search should explore the heuristic search space as widely as possible within a limited searching time. This simple and general graph based hyperheuristic may be applied to a range of timetabling and optimisation problems.