8 Working set algorithm
The computational approach maintains a list of convex polygons, the working set, with the invariant that every Moser set of area below the threshold contains (a rigid motion of) at least one polygon in the list.
A working set is a list of convex polygons. Intended invariants:
every polygon in the list contains a copy of the initial worm (Definition 28) under some direct isometry;
every Moser set of area strictly less than \(A_*\) contains a copy of some polygon in the list under some direct isometry.
Invariant 1 is currently a convention maintained by construction; Invariant 2 is the core correctness statement the algorithm preserves.
The initial working set contains exactly the initial worm.
The minimum area in a working set is the minimum of the shoelace areas of its polygons (taken as \(0\) on the empty set).