McMillan's area problem.

A Minimal Area Problem for Nonvanishing Functions

The minimal area covered by the image of the unit disk is found for nonvanishing univalent functions normalized by the conditions f(0) = 1, f ′(0) = α. Two different approaches are discussed, each of which contributes to the complete solution of the problem. The first approach reduces the problem, via symmetrization, to the class of typically real functions, where the well-known integral repres...

The minimum area spanning tree problem

Motivated by optimization problems in sensor coverage, we formulate and study the Minimum-Area Spanning Tree (mast) problem: Given a set P of n points in the plane, find a spanning tree of P of minimum “area,” where the area of a spanning tree T is the area of the union of the n − 1 disks whose diameters are the edges in T . We prove that the Euclidean minimum spanning tree of P is a constant-f...

1 Delimitation of the Research Problem Area

Two Techniques in the Area of the Star Problem

Decidability of the Star Problem, the problem whether the language IP is recognizable for a recognizable language IP, remains open. We slightly generalize the problem and show that then its decidability status depends strongly on the assumptions considering the trace monoid and niteness of IP. More precisely, we show that for nite set IP fA; Bg fCg and recognizable IR it is decidable whether IP...

Trees, slices, and wheels: On the floorplan area minimization problem

Hierarchical approaches to floorplan design usually use trees to represent hierarchical floorplans, defining topological relations between a set of components to be placed on a (circuit) board. This placement is then optimized to minimize chip area, perimeter, or other such cost measurements. This work places the problem of minimizing hierarchical floorplans of order k within the appropriate th...