Permutation Classes of Polynomial Growth

A pattern class is a set of permutations closed under the formation of subpermutations. Such classes can be characterised as those permutations not involving a particular set of forbidden permutations. A simple collection of necessary and sufficient conditions on sets of forbidden permutations which ensure that the associated pattern class is of polynomial growth is determined. A catalogue of all such sets of forbidden permutations having three or fewer elements is provided together with bounds on the degrees of the associated enumerating polynomials.Comment: 17 pages, 4 figure

Sorting with a forklift

A fork stack is a generalised stack which allows pushes and pops of several items at a time. We consider the problem of determining which input streams can be sorted using a single forkstack, or dually, which permutations of a fixed input stream can be produced using a single forkstack. An algorithm is given to solve the sorting problem and the minimal unsortable sequences are found. The results are extended to fork stacks where there are bounds on how many items can be pushed and popped at one time. In this context we also establish how to enumerate the collection of sortable sequences.Comment: 24 pages, 2 figure

Pattern classes and priority queues

When a set of permutations comprising a pattern class C is submitted as input to a priority queue the resulting output is again a pattern class C'. The basis of C' is determined for pattern classes C whose basis elements have length 3, and is finite in these cases. An example is given of a class C with basis 2431 for which C is not finitely based

The use of function points to find cost analogies

Finding effective techniques for the early estimation of project effort remains an important — and frustratingly elusive — research objective for the software development community. We have conducted an empirical study of 21 real time projects for a major software developer. The study collected a range of counts and measures derived from specification documents, including a derivative of Function Points intended for highly constrained systems. Notwithstanding the fact that the projects were drawn from a comparatively stable environment, traditional approaches for building prediction systems, (for example, regression analysis) failed to yield a useful predictive model. By contrast, estimation based upon the automated search for analogous projects produced more accurate estimates. How much this is a characteristic of this particular dataset and how much these findings might be more generally replicated is uncertain. Nevertheless, these results should act as encouragement for follow up research on a much under utilised estimation technique