arXiv subjects

Dana Jansens

Publications and source records attributed to Dana Jansens.

2 recordsLinked to original sources

arXiv2012

Making triangulations 4-connected using flips

We show that any combinatorial triangulation on n vertices can be transformed into a 4-connected one using at most floor((3n - 9)/5) edge flips. We also give an example of an infinite family of triangulations that requires this many flips to be made 4-connected, showing that our bound is tight. In addition, for n >= 19, we improve the upper bound on the number of flips required to transform any 4-connected triangulation into the canonical triangulation (the triangulation with two dominant vertices), matching the known lower bound of 2n - 15. Our results imply a new upper bound on the diameter of the flip graph of 5.2n - 33.6, improving on the previous best known bound of 6n - 30.

cs.CG↗

arXiv2010

Improved Methods For Generating Quasi-Gray Codes

Consider a sequence of bit strings of length d, such that each string differs from the next in a constant number of bits. We call this sequence a quasi-Gray code. We examine the problem of efficiently generating such codes, by considering the number of bits read and written at each generating step, the average number of bits read while generating the entire code, and the number of strings generated in the code. Our results give a trade-off between these constraints, and present algorithms that do less work on average than previous results, and that increase the number of bit strings generated.

cs.DM↗