TY - CHAP
AB - The Morse-Smale complex can be either explicitly or implicitly represented. Depending on the type of representation, the simplification of the Morse-Smale complex works differently. In the explicit representation, the Morse-Smale complex is directly simplified by explicitly reconnecting the critical points during the simplification. In the implicit representation, on the other hand, the Morse-Smale complex is given by a combinatorial gradient field. In this setting, the simplification changes the combinatorial flow, which yields an indirect simplification of the Morse-Smale complex. The topological complexity of the Morse-Smale complex is reduced in both representations. However, the simplifications generally yield different results. In this chapter, we emphasize properties of the two representations that cause these differences. We also provide a complexity analysis of the two schemes with respect to running time and memory consumption.
AU - Günther, David
AU - Reininghaus, Jan
AU - Seidel, Hans-Peter
AU - Weinkauf, Tino
ED - Bremer, Peer-Timo
ED - Hotz, Ingrid
ED - Pascucci, Valerio
ED - Peikert, Ronald
ID - 10817
SN - 1612-3786
T2 - Topological Methods in Data Analysis and Visualization III.
TI - Notes on the simplification of the Morse-Smale complex
ER -