The Reeb Structure of Bend Distance in Grid Domains: Cycle Bounds with Holes, Exact Sector Geometry on Disks, and the Two-Port Constant $c_2^{\square }=3$

Aoji Li, Guangbo Ding

The fixed-parameter algorithm for coordinated motion planning on discretized simple polygons (ICALP 2026) rests on a single-port sector decomposition: grid vertices are labelled by…