5 papers
Flip Distance of Non-Crossing Spanning Trees: NP-Hardness and Improved Bounds
HÃ¥vard Bakke Bjerkevik, Joseph Dorfer, Linda Kleist +2
We consider the problem of reconfiguring non-crossing spanning trees on point sets. For a set of points in general position in the plane, the flip graph has a vertex…
Counting Barcodes with the same Betti Curve
Henry Ashley, HÃ¥vard Bakke Bjerkevik, Justin Curry +2
This paper considers an important inverse problem in topological data analysis (TDA): How many different barcodes produce the same Betti curve? Equivalently, given a function $β\c…
Reeb Graph of Sample Thickenings
HÃ¥vard Bakke Bjerkevik, Nello Blaser, Lars M. Salbu
We consider the Reeb graph of a thickening of points sampled from an unknown space. Our main contribution is a framework to transfer reconstruction results similar to the well-know…
Stabilizing decomposition of multiparameter persistence modules
HÃ¥vard Bakke Bjerkevik
While decomposition of one-parameter persistence modules behaves nicely, as demonstrated by the algebraic stability theorem, decomposition of multiparameter modules is known to be…
Flipping Non-Crossing Spanning Trees
HÃ¥vard Bakke Bjerkevik, Linda Kleist, Torsten Ueckerdt +1
For a set of points in general position in the plane, the flip graph has a vertex for each non-crossing spanning tree on and an edge between any two spanning tre…