These research papers consider the problem of placing two-dimensional deformable discs of equal size within a rigid boundary. Two cases are distinguished, depending on whether the disc is small compared with the overall area of the bounded region. The former case is covered by the first paper; the problem is essentially one of packing deformable spheres in an unbounded case, the boundary phenomena being irrelevant. The latter case is covered by the second paper, on using simulated annealing.

Some assumptions have to be made about the forces required to move or deform the discs, but the basic result of the first paper is that a hexagonal pattern for the cutting of the discs with appropriate distortion differs by at most a factor of 1.1 from an optimal pattern. An estimate is given for this general problem in terms of appropriate measures of deformability.

In the second paper, the authors have to contend with the forces produced by the boundary. A good algorithm is given for computing a solution efficiently depending on the cooling schedule used.

The results have potential wide applicability in engineering and are well grounded in numerical practice. The papers are well written, well laid out, and accessible, but contain a lot of mathematical detail. The illustrations are effective in showing what is actually going on, especially in the second paper. The references are helpful. The results, while not wholly surprising, are sufficiently good to warrant further consideration of the algorithms.