← 研踪 PaperTrailarXiv:2610.16025 · v2
QPTAS for Max Weight Independent Set in Graphs with Strongly Edge-Sublinear Separators
首次提交 2026-10-12 08:52
版本更新 2026-11-03 07:50
雷达观测 2026-11-04 23:40
摘要
A hereditary graph class has strongly edge-sublinear separators if, for some constant $0 \leqslant b < 1$, every graph in the class with $m$ edges admits a balanced separator of size $\mathcal O(m^b)$. We show that Max Weight Independent Set (MWIS) admits a deterministic quasipolynomial-time approximation scheme (QPTAS) on every such class. In particular, this applies to graphs excluding any fixed graph as an induced minor, by a separator theorem of Korhonen and Lokshtanov [SODA 2024]. Our theorem generalizes the QPTASes for axis-parallel rectangles [Adamaszek and Wiese, FOCS 2013] and polygons [Adamaszek, Har-Peled, and Wiese, JACM 2019], or equivalently for packing connected subgraphs of a planar graph [Pilipczuk, van Leeuwen, and Wiese, Algorithmica 2020]. It also generalizes the QPTAS for MWIS on hereditary classes with strongly sublinear separators measured in vertices [Dvořák, EJC 2018; Dvořák and Lahiri, ESA 2021], as well as the QPTASes for graphs excluding specific induced minors [Chudnovsky et al., arXiv 2025; Bonnet et al., SWAT 2026; Czyżewska et al., arXiv 2026].
作者备注：23 pages
观测到的版本
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v2 · 2026-11-03 07:50 · 最新观测版本
QPTAS for Max Weight Independent Set in Graphs with Strongly Edge-Sublinear Separators
A hereditary graph class has strongly edge-sublinear separators if, for some constant $0 \leqslant b < 1$, every graph in the class with $m$ edges admits a balanced separator of size $\mathcal O(m^b)$. We show that Max Weight Independent Set (MWIS) admits a deterministic quasipolynomial-time approximation scheme (QPTAS) on every such class. In particular, this applies to graphs excluding any fixed graph as an induced minor, by a separator theorem of Korhonen and Lokshtanov [SODA 2024]. Our theorem generalizes the QPTASes for axis-parallel rectangles [Adamaszek and Wiese, FOCS 2013] and polygons [Adamaszek, Har-Peled, and Wiese, JACM 2019], or equivalently for packing connected subgraphs of a planar graph [Pilipczuk, van Leeuwen, and Wiese, Algorithmica 2020]. It also generalizes the QPTAS for MWIS on hereditary classes with strongly sublinear separators measured in vertices [Dvořák, EJC 2018; Dvořák and Lahiri, ESA 2021], as well as the QPTASes for graphs excluding specific induced minors [Chudnovsky et al., arXiv 2025; Bonnet et al., SWAT 2026; Czyżewska et al., arXiv 2026].
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