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In an exploration paper, {\it L. Chen, Algorithms for Deforming andContracting Simply Connected Discrete Closed Manifolds (I)}, we designedalgorithms for deforming and contracting a simply connected discrete closedmanifold to a discrete sphere. However, the algorithms could not guarantee tobe applicable to every case. This paper will be the continuation of theexploration.  This paper contains two main procedures: (1) A shrinking procedure tocontract a simply connected closed manifold. Unlike ones in the previous paper,we added a tree structure to support the process. (2) A more direct procedurefor mapping a component from a separated simply connected closed manifold to adisk.  We also discuss the practical use of these algorithms in topological dataanalysis. We think that we have an algorithmic solution, but careful detailedanalysis should be done next.

Algorithms for Deforming and Contracting Simply Connected Discrete Closed Manifolds (II)