Carlos Hoppen - The analysis of a prioritised probabilistic algorithm to find large induced forests in regular graphs with large girth

dmtcs:2769 - Discrete Mathematics & Theoretical Computer Science, January 1, 2010, DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10) - https://doi.org/10.46298/dmtcs.2769
The analysis of a prioritised probabilistic algorithm to find large induced forests in regular graphs with large girthArticle

Authors: Carlos Hoppen 1

  • 1 Instituto de Matematica [Porto Alegre, RS]

The analysis of probabilistic algorithms has proved to be very successful for finding asymptotic bounds on parameters of random regular graphs. In this paper, we show that similar ideas may be used to obtain deterministic bounds for one such parameter in the case of regular graphs with large girth. More precisely, we address the problem of finding a large induced forest in a graph $G$, by which we mean an acyclic induced subgraph of $G$ with a lot of vertices. For a fixed integer $r \geq 3$, we obtain new lower bounds on the size of a maximum induced forest in graphs with maximum degree $r$ and large girth. These bounds are derived from the solution of a system of differential equations that arises naturally in the analysis of an iterative probabilistic procedure to generate an induced forest in a graph. Numerical approximations suggest that these bounds improve substantially the best previous bounds. Moreover, they improve previous asymptotic lower bounds on the size of a maximum induced forest in a random regular graph.


Volume: DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10)
Section: Proceedings
Published on: January 1, 2010
Imported on: January 31, 2017
Keywords: Probabilistic algorithms,graphs,large girth,[INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[INFO.INFO-CG] Computer Science [cs]/Computational Geometry [cs.CG]

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