苗条的树木切割宽度的宽度
Robert Ganian1, Viktoriia Korchemna1
1Algorithms and Complexity Group, TU Wien, Vienna, Austria.
Algorithmica
|July 29, 2024
概括
介绍了纤细的树木切割宽度,一个新的图形参数,弥合了树木宽度的边缘切割类型的结构和算法需求. 这个参数为现有方法提供了一个不那么严格的替代方案.
科学领域:
- 图形理论 图形理论
- 理论计算机科学 理论计算机科学
- 算法算法是一种算法.
背景情况:
- 树幅是一个基本的图形参数,具有广泛的算法应用.
- 现有的边缘切割类似物,如树切割宽度和边缘切割宽度,在结构性质或算法实用性方面都有局限性.
- 需要一个统一的参数来捕捉边缘切割的结构和算法方面.
研究的目的:
- 介绍和分析一个新的图形参数",细木切割宽度",作为边缘切割树宽度的潜在模拟.
- 证明细木切割宽度满足结构和算法要求,克服了以前参数的局限性.
- 提供有效的方法来计算和表征细木砍伐宽度.
主要方法:
- 通过调整分解中薄节点的门来修改砍伐树的宽度.
- 开发使用跨树分解的替代性表征.
- 通过禁止的沉浸关系进行表征.
- 设计一个近似算法来计算参数.
主要成果:
- 苗条的树木切割宽度被证明是一个有效的基于边缘切割的树木宽度模拟,具有理想的结构和算法特性.
- 它比最近引入的边缘切割宽度更少限制.
- 通过跨树分解建立了另一种表征,简化了它的可用性.
- 禁止沉浸的表征和近似算法被介绍.
结论:
- 苗条的树木切割宽度成功地整合了先前参数的理想特性,提供了一个强大的替代方案.
- 这个新参数对算法图形理论和相关领域具有重大前景.
- 这些发现为新的应用和对图形分解技术的更深入理解铺平了道路.
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