Bi-Weekly Talk: Janosch Fuchs: The Slotted Online One-Sided Crossing Minimization Problem on 2-Regular Graphs

Wednesday, July 06, 2022, 10:30am

Location: RWTH Aachen University, Department of Computer Science - Ahornstr. 55, building E3, room 9u10
and as Online session

Speaker: Janosch Fuchs



In the area of graph drawing, the One-Sided Crossing Minimization Problem (OSCM) is defined on a bipartite graph with both vertex sets aligned parallel to each other and all edges being drawn as straight lines.  The task is to find a permutation of one of the node sets such that the total number of all edge-edge intersections, called \emph{crossings}, is minimized.  Usually, the degree of the nodes of one set is limited by some constant k, with the problem then abbreviated to OSCM-k.

We study an online variant of this problem, in which one of the node sets is already given. The other node set and the incident edges are revealed iteratively as requests and each node has to be inserted into placeholders, which we call "slots".  The number of slots coincides with the number of requests and their order is fixed. The goal is again to minimize the number of crossings in the final graph. Minimizing crossings in an online way is related to the more empirical field of dynamic graph drawing. Note that the slotted OSCM problem is harder to solve for an online algorithm but in the offline case it is equivalent to the version without slots.