Problem solving techniques for the design of algorithms

By studying the problem-solving techniques that people use to design algor i thms we can learn something about bui ld ing systems that automatical ly derive algor i thms or assist human designers. In this paper we present a model of a lgor i thm design based on our analysis of the protocols of two subjects designing three convex hull algori thms. The subjects work mainly in a data-f low problem space in wh ich the objects are representat ions of partially specif ied algori thms. A small number of general-purpose operators construct and modify the representat ions; these operators are adapted to the current problem state by means-ends analysis. The problem space also includes knowledge-r ich schemas such as divide and conquer that subjects incorporate into their algori thms. A part icularly versati le problem-solving method in this problem space is symbolic execut ion, wh ich can be used to refine, verify, or explain components of an algor i thm. The subjects also work in a task-domain space about geometry. The interplay between problem solving in the two spaces makes possible the process of discovery. We have observed that the t ime a subject takes to design an algori thm is proport ional to the number of components in the algor i thm's data-f low representat ion. Finally, the detai ls of the problem spaces provide a model for bui lding a robust automated system. This research is suppor ted by the Defense Advanced Research Projects Agency (DOD), ARPA Order No. 3597, moni tored by the Air Force Avionics Laboratory Under Contract F33615-81-K-1539. The views and conclus ions contained in this document are those of the authors and should not be interpreted as representing the off icial pol icies, either expressed or impl ied, of the Defense Advanced Research Projects Agency or the U.S. Government. Table of