Local Optimization Algorithms for Maximum Planar Subgraph - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2024

Local Optimization Algorithms for Maximum Planar Subgraph

Résumé

Consider the NP-hard problem of, given a simple graph G, to find a planar subgraph of G with the maximum number of edges. This is called the Maximum Planar Subgraph problem and the best known approximation is (4/9) and is obtained by sophisticated Graphic Matroid Parity algorithms. Here we show that applying a local optimization phase to the output of this known algorithm improves this approximation ratio by a small epsilon > 0. A second local optimization algorithm achieves a tight ratio of (5/12) for Maximum Planar Subgraph without using Matroid Parity. We also show that applying a greedy algorithm before this second optimization algorithm improves its ratio to at least (91/216) < (4/9).
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Dates et versions

hal-04629835 , version 1 (30-06-2024)
hal-04629835 , version 2 (13-08-2024)

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Gruia Călinescu, Sumedha Uniyal. Local Optimization Algorithms for Maximum Planar Subgraph. 2024. ⟨hal-04629835v1⟩
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