R. Geoff Dromey

Exploiting partial order with quicksort

The widely known Quicksort algorithm does not attempt to actively take advantage of partial order in sorting data. A simple change can be made to the Quicksort strategy to give a bestcase performance of n, for ordered data, with a smooth transition to O(n log n) for random data. This algorithm (Transort) matches the performance of Sedgewicks claimed best implementation of Quicksort for random data.

Optimum scaling of mass spectra for computer-matching

Abstract A scaling procedure that minimizes effects caused by mass discrimination-and other instrumental distortion in computer-matching of mass spectra is described. It is shown how spectra should be matched only when they have been scaled to be at their minimum “distance” with respect to the similarity index in use for the measurement.

Forced termination of loops

Loops must often be forced to terminate early. Solutions to such problems are usually either language‐dependent or rather clumsy. A practical alternative is presented. The accompanying methodology clarifies the role of the finalization mechanism in loop construction. It also leads to the idea of control‐structure independence in the context of data representation and forced termination.

Program development by inductive stepwise refinement

A constructive method of program development is presented. It seeks to unify two important ideas about program development. Namely that programming is a goal‐oriented activity and that there should be a correspondence between data and program structures. The latter concept is seen to be extensible beyond the data processing context in which it was originally proposed. Induction provides the vehicle for program development by stepwise refinement, with the final program being constructed by application of a sequence of progressively more powerful generalizations. The design process employed guarantees the correctness of the final program provided that each of the refinement steps have been correctly taken. The method is illustrated by a number of samples.

Fast string searching by finding subkeys in subtext

‘I he string warch problem is defined as follows. Given rwo seqllences of characters, a text of n characfClS T = <t 1, t2, t3, ..,, tn> and a key of m characters K = Ckl, k2. kS, .,., km) chosen from an alphabet of q characters A = {al, a2, ..,, aq), find all indices i such that ti = kl , t(s t 1) := k2, ..,, t(i + m 1) = km. That IS. fmd aii %Jbstrings in the text which match the key. Overlapping substrings ar+: t.o be found. Thus ‘aa’ is mat&ed at 3 positions in ‘aasbaa’. Many variations of this problem exist. Only the t Irst occurrcncc of the key may be needed. There may hc rwrc than one key. The text and keys may be rn~Jlridimcnsiollal. ‘I he ‘naive’ solution is to position the key successively at each text p&ion and check for a match. If the key never (.)ccurs in the tex,t alI text characters (e.xcept perhaps the last m 1) are checked at least mcc and. if matches to prefixes df the key appear, rnz~sy text characters are checked more than once. In