On Embedding an OuterPlanar Graph in a Point SetBose, Prosenjit (1998) On Embedding an OuterPlanar Graph in a Point Set. In: Graph Drawing 5th International Symposium, GD '97, September 1820, 1997 , pp. 2536(Official URL: http://dx.doi.org/10.1007/3540639381_47). Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/3540639381_47
AbstractGiven an nvertex outerplanar graph G and a set P of n points in the plane, we present an O(n log³ n) time and O(n) space algorithm to compute a straightline embedding of G in P, improving upon the algorithm in [GMPP91, CU96] that requires O(n²) time. Our algorithm is nearoptimal as there is an \Omega (n log n) lower bound for the problem [BMS95]. We present a simpler O(nd) time and an O(n) space algorithm to compute a straightline embedding of G in P where log n \leq d \leq 2n is the lenght of the longest vertex disjoint path in the dual of G. Therefore, the time complexity of the simpler algorithm varies between O(n log n) and O(n²) depending on the value of d. More efficient algorithms are presented for certain restricted cases. If the dual of G is a path, then an optimal \theta (n log n) time algorithm is presented. If the given point set is in convex position then we show that O(n) time suffices.
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