136 research outputs found
A Note on the Practicality of Maximal Planar Subgraph Algorithms
Given a graph , the NP-hard Maximum Planar Subgraph problem (MPS) asks for
a planar subgraph of with the maximum number of edges. There are several
heuristic, approximative, and exact algorithms to tackle the problem, but---to
the best of our knowledge---they have never been compared competitively in
practice. We report on an exploratory study on the relative merits of the
diverse approaches, focusing on practical runtime, solution quality, and
implementation complexity. Surprisingly, a seemingly only theoretically strong
approximation forms the building block of the strongest choice.Comment: Appears in the Proceedings of the 24th International Symposium on
Graph Drawing and Network Visualization (GD 2016
Preferential attachment without vertex growth: emergence of the giant component
We study the following preferential attachment variant of the classical
Erdos-Renyi random graph process. Starting with an empty graph on n vertices,
new edges are added one-by-one, and each time an edge is chosen with
probability roughly proportional to the product of the current degrees of its
endpoints (note that the vertex set is fixed). We determine the asymptotic size
of the giant component in the supercritical phase, confirming a conjecture of
Pittel from 2010. Our proof uses a simple method: we condition on the vertex
degrees (of a multigraph variant), and use known results for the configuration
model.Comment: 20 page
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