← 研踪 PaperTrailarXiv:2611.01796 · v2
Exact Tie-Breaking and Tight Degree Bounds for Minimum-Degree Greedy on Interval Graphs
首次提交 2026-11-01 19:04
版本更新 2026-11-03 16:36
雷达观测 2026-11-04 23:39
摘要
We study tie-breaking in the minimum-degree greedy algorithm (MDG) for maximum independent set on interval graphs. Given an interval representation of an $n$-vertex graph, we compute the largest and smallest output sizes and construct executions attaining them in $O(n^3)$ time and $O(n^2)$ space. For maximum degree at most four, favorable tie-breaking gives a tight guarantee of $3/4$. For every maximum-degree bound of at least five, the guarantee drops to $2/3$. Both bounds are tight even on connected unit interval graphs whose output size is independent of tie-breaking. Together with the known optimality of favorable tie-breaking for maximum degree at most three, these results give a complete classification by degree bound.
作者备注：23 pages, 3 figures
观测到的版本
相邻记录可能跳过中间版本；首次发现 v2 及以上也会标为版本更新。
v2 · 2026-11-03 16:36 · 最新观测版本
Exact Tie-Breaking and Tight Degree Bounds for Minimum-Degree Greedy on Interval Graphs
We study tie-breaking in the minimum-degree greedy algorithm (MDG) for maximum independent set on interval graphs. Given an interval representation of an $n$-vertex graph, we compute the largest and smallest output sizes and construct executions attaining them in $O(n^3)$ time and $O(n^2)$ space. For maximum degree at most four, favorable tie-breaking gives a tight guarantee of $3/4$. For every maximum-degree bound of at least five, the guarantee drops to $2/3$. Both bounds are tight even on connected unit interval graphs whose output size is independent of tie-breaking. Together with the known optimality of favorable tie-breaking for maximum degree at most three, these results give a complete classification by degree bound.
查看此版本解读 →查看此版本原文 ↗