Abstract not found

When computer scientists discuss the computational complexity of, for example, finding the shortest path from building A to building B in some town or city, their starting point typically is a formal description of the problem at hand, e.g., a graph with weights on every edge where buildings correspond to vertices, routes between buildings to edges, and route-distances to edge-weights. Given such a formal description, either tractability or intractability of the problem is established, by proving that the problem either enjoys a polynomial time algorithm or is NP-hard. However, this problem description is in fact an abstraction of the actual problem of being in A and desiring to go to B: it focuses on the relevant aspects of the problem (e.g., distances between landmarks and crossings) and leaves out a lot of irrelevant details. This abstraction step is often overlooked, but may well contribute to the overall complexity of solving the problem at hand. For example, it appears that “going from A to B ” is rather easy to abstract: it is fairly clear that the distance between A and the next crossing is relevant, and that the color of the roof of B is typically not. However, when the

journal homepage: www.elsevier.com/locate/jecp Using the axis of elongation to align shapes: