Computing area in presentations of the trivial group

In the first of these two cases, area was studied under the name by Majumdar, Robbins and Zyskin in the context of the design of liquid crystals. We explain how the problem of calculating it can be reinterpreted in terms of RNA-folding. In the second, area is what Jiang called and studied when counting fixed points for self-maps of a compact surface, considered up to homotopy. In 1991 Grigorchuk and Kurchanov gave an algorithm computing width and asked whether it could be improved to polynomial-time. We answer this affirmatively.]]>