Algorithmic aspects of alternating sum of volumes. Part 2: Nonconvergence and its remedy

The paper Js the second part of a 2-part paper The first part focused on the ~ssues of data structure and fast difference operation_ The second studies the nonconvergence of the alternating sum of volumes (ASV) process. An ASV ~s a series of convex components fomed by alternating umon and d~fference operattons It ~s desJrable that an ASV series be finite However, such ~s not always the case the ASV algonthm can be nonconvergent The paper ~nvestigates the causes of th~s nonconvergence, and finds and proves the conditions responsible for ~t L~near t~me algonthms are then developed for detection