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If K is a finite simplicial complex and h is an injective map from the vertices of K to R we show how to extend h to a discrete Morse function in the sense of Forman [F2] in a reasonably efficient manner so that the resulting discrete Morse function mirrors the large-scale behavior of h. A concrete algorithm is given for the case where K is a subcomplex of R 3 . Date: January 21, 2005. 2000 Mathematics Subject Classification. Primary: 57Q99 68U05. Secondary: 57R70 58E05 65D18 65R99.doi:10.1080/10586458.2005.10128941 fatcat:qprm6ub4wbbwlcfqrkjz4flhai