We present the first polynomial-time algorithm to solve the maximum weight independent set problem for apple-free graphs, which is a common generalization of several important classes where the problem can be solved efficiently, such as claw-free graphs, chordal graphs, and cographs. Our solution is based on a combination of two algorithmic techniques (modular decomposition and decomposition by clique separators) and a deep combinatorial analysis of the structure of apple-free graphs. Our algorithm is robust in the sense that it does not require the input graph $G$ to be apple-free; the algorithm either finds an independent set of maximum weight in $G$ or reports that $G$ is not apple-free.

Independent sets of maximum weight in apple-free graphs

MOSCA, Raffaele
2010-01-01

Abstract

We present the first polynomial-time algorithm to solve the maximum weight independent set problem for apple-free graphs, which is a common generalization of several important classes where the problem can be solved efficiently, such as claw-free graphs, chordal graphs, and cographs. Our solution is based on a combination of two algorithmic techniques (modular decomposition and decomposition by clique separators) and a deep combinatorial analysis of the structure of apple-free graphs. Our algorithm is robust in the sense that it does not require the input graph $G$ to be apple-free; the algorithm either finds an independent set of maximum weight in $G$ or reports that $G$ is not apple-free.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11564/214764
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