In this article we prove that the minimum-degree greedy algorithm, with adversarial tie-breaking, is a $(2/3)$-approximation for the Maximum Independent Set problem on interval graphs. We show that this is tight, even on unit interval graphs of maximum degree 3. We show that on chordal graphs, the greedy algorithm is a $(1/2)$-approximation and that this is again tight. These results contrast with the known (tight) approximation ratio of $\frac{3}{\Delta+2}$ of the greedy algorithm for general graphs of maximum degree $\Delta$.

翻译：本文证明了最小度贪心算法（采用对抗性平局处理）在区间图上的最大独立集问题中具有$(2/3)$-近似比。我们证明该界是紧的，即使在最大度为3的单位区间图上也是如此。我们进一步表明，在弦图上该贪心算法具有$(1/2)$-近似比，且该界同样是紧的。这些结果与已知的贪心算法在最大度为$\Delta$的一般图上的$\frac{3}{\Delta+2}$紧近似比形成对比。