IMPROVED ALGORITHMS FOR THE POINT-SET EMBEDDABILITY PROBLEM FOR PLANE 3-TREES
Tanaeem M. Moosa, M. Sohel Rahman · Discrete Mathematics Algorithms and Applications · 2012
In the point-set embeddability problem, we are given a plane graph G with n vertices and a point set S with the same number of points. Now the goal is to answer the question whether there exists a straight-line drawing of G such that each vertex is represented as a distinct point of S as well as to provide an embedding if one does exist. This problem has recently been solved in O(n2 log n) time for plane 3-trees. In this paper, we present a new efficient algorithm with time complexity O(n4/3+ϵ log n). We also present an O(nk4) time algorithm for the case when |S| = k > n. This is a significant improvement over the best algorithm for this case in the literature, which runs in O(nk8) time.