Основные понятия
Greedy algorithm is a (2/3)-approximation for Maximum Independent Set on interval graphs and a (1/2)-approximation on chordal graphs.
Аннотация
The article discusses the approximation ratio of the minimum-degree greedy algorithm for the Maximum Independent Set problem on interval and chordal graphs. It proves that the algorithm is a (2/3)-approximation for interval graphs, even on unit interval graphs of maximum degree 3, and a (1/2)-approximation for chordal graphs. The results contrast with the known approximation ratio of 3∆+2 for general graphs. The study focuses on worst-case tie-breaking scenarios to analyze how close the Greedy algorithm comes to computing a maximum independent set. It also delves into tree decompositions, simplicial vertices, and various observations related to Greedy's performance on different graph types.
Статистика
Greedy is a (2/3)-approximation for Maximum Independent Set on interval graphs.
Greedy is a (1/2)-approximation for Maximum Independent Set on chordal graphs.
Approximation ratio of 3∆+2 for general graphs.
Цитаты
"The minimum-degree greedy algorithm is a (2/3)-approximation for the Maximum Independent Set problem on interval graphs."
"Greedy is a (1/2)-approximation algorithm on chordal graphs."