Non-planar core reduction of graphs

A Note on the Practicality of Maximal Planar Subgraph Algorithms

“…Our results confirm the need for heuristic approaches, as ILP solves less than 25% of the larger graphs of the (comparably simple) Rome set within 10min. Even deploying strong preprocessing [6] (+PP) and doubling the computation time does not help significantly, cf. Fig.…”

“…When discussing implementation complexity, it seems safe to assume that a programmer will already start off with some kind of graph library for her basic datastructure needs. 6 In the context of the ILP-based approach, we assume that the programmer uses one of the various freely available (or commercial) frameworks. Writing a competitive branch-and-cut framework from ground up would require a staggering amount of knowledge, experience, time, and finesse.…”

“…This measure is still intrinsically subjective (although we feel that the situation is quite clear in most cases), and opinions may vary depending on the implementor's knowledge, experience, etc. We discuss these issues when they become relevant 6. Many freely available graph libraries contain linear-time planarity tests.…”

Crossing Minimization meets Simultaneous Drawing

“…These transformations are done in such a way that the crossing number of the original graph and of the transformed graph are equal. For example, Chimani and Gutwenger [6] developed a non-planar core reduction that yields a significant speed-up in practical crossing minimization computations. However, these graph reduction techniques cannot be used for simultaneous crossing minimization in general.…”

Exact Algorithms for the Maximum Planar Subgraph Problem

“…We assume our input graph G to be biconnected non-planar, with edge weights w : E(G) → N and minimum node degree 3. This can be achieved in linear time using the Non-Planar Core reduction [7] as a preprocessing, without changing the graph's skewness.…”