Pessimal guesses may be optimal: a counterintuitive search result

Abstract

A particular style of search is considered that is motivated by the problem of reconstructing the surface of three-dimensional objects given a collection of planar contours representing cross-sections through the objects. An improvement on the simple divide-and-conquer method is presented. The key idea is to locate bottlenecks (minimal separators), which markedly reduces the number of searches required but reduces other measures (e.g. nodes expanded) by only a constant factor. It is observed that for well-behaved search spaces, the search efficiency can be improved further by making 'pessimal guesses'. This suggests a style of search in which the region of the search space thought to be close to the optimal solution (on whatever grounds are available) is examined last, while the outlying regions (the pessimal guesses) are examined first.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>