Given a graph G with It vertices and a set S of n points in the plane, a point-set embedding of G on S is a planar drawing such that each vertex of G is mapped to a distinct point of S. A geometric point-set embedding is a point-set embedding with no edge bends. This paper studies the following problem: The input is a set S of n points, a planar graph G with n vertices, and a geometric point-set embedding of a subgraph G' c G on a subset of S. The desired output is a point-set embedding of G on S that includes the given partial drawing of G'. We concentrate on trees and show how to compute the output in O(n(2) log n) time in a real-RAM model and with at most n - k edges with at most 1 + 2[k/2] bends, where k is the number of vertices of the given subdrawing. We also prove that there are instances of the problem which require at least k - 3 bends on n - k edges.
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