
Universität Bonn > Institut für Informatik > Abteilung V  
CSReports 2017  Copyright 2017 Universität Bonn, Institut für Informatik, Abt. V  
85365 13.05.2017 
A QPTAS for the Base of the Number of CrossingFree Structures on a Planar Point Set (revised version)
Marek Karpinski, Andrzej Lingas, Dzmitry Sledneu [Download PostScript] [Download PDF] The number of triangulations of a planar n point set S is known to be c^n , where the base c lies between 2.43 and 30 . Similarly, the number of crossingfree spanning trees on S is known to be d^n , where the base d lies between 6.75 and 141.07 . The fastest known algorithm for counting triangulations of S runs in O^∗ (2^n) time while that for counting crossingfree spanning trees runs in O^∗ (7.125^n ) time. The fastest known arbitrarily close approximation algorithms for the base of the number of triangulations of S and the base of the number of crossingfree spanning trees of S , respectively, run in time subexponential in n . We present the first quasipolynomial approximation schemes for the base of the number of triangulations of S and the base of the number of crossingfree spanning trees on S , respectively. 

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Universität Bonn > Institut für Informatik > Abteilung V 