arXiv subjects

Naoki Katoh

Publications and source records attributed to Naoki Katoh.

20 records · Page 2Linked to original sources

arXiv2006

Enumerating Constrained Non-crossing Minimally Rigid Frameworks

In this paper we present an algorithm for enumerating without repetitions all the non-crossing generically minimally rigid bar-and-joint frameworks under edge constraints (also called constrained non-crossing Laman frameworks) on a given generic set of $n$ points. Our algorithm is based on the reverse search paradigm of Avis and Fukuda. It generates each output graph in $O(n^4)$ time and O(n) space, or, slightly different implementation, in $O(n^3)$ time and $O(n^2)$ space. In particular, we obtain that the set of all the constrained non-crossing Laman frameworks on a given point set is connected by flips which restore the Laman property.

math.CO↗

arXiv2001

Notes on computing peaks in k-levels and parametric spanning trees

We give an algorithm to compute all the local peaks in the $k$-level of an arrangement of $n$ lines in $O(n \log n) + \tilde{O}((kn)^{2/3})$ time. We can also find $τ$ largest peaks in $O(n \log ^2 n) + \tilde{O}((τn)^{2/3})$ time. Moreover, we consider the longest edge in a parametric minimum spanning tree (in other words, a bottleneck edge for connectivity), and give an algorithm to compute the parameter value (within a given interval) maximizing/minimizing the length of the longest edge in MST. The time complexity is $\tilde{O}(n^{8/7}k^{1/7} + n k^{1/3})$

cs.CG↗