eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-12-13
8:1
8:15
10.4230/LIPIcs.IPEC.2023.8
article
Stretch-Width
Bonnet, Édouard
1
https://orcid.org/0000-0002-1653-5822
Duron, Julien
1
https://orcid.org/0009-0004-0925-9438
Univ Lyon, CNRS, ENS de Lyon, Université Claude Bernard Lyon 1, LIP UMR5668, France
We introduce a new parameter, called stretch-width, that we show sits strictly between clique-width and twin-width. Unlike the reduced parameters [BKW '22], planar graphs and polynomial subdivisions do not have bounded stretch-width. This leaves open the possibility of efficient algorithms for a broad fragment of problems within Monadic Second-Order (MSO) logic on graphs of bounded stretch-width. In this direction, we prove that graphs of bounded maximum degree and bounded stretch-width have at most logarithmic treewidth. As a consequence, in classes of bounded stretch-width, Maximum Independent Set can be solved in subexponential time 2^{Õ(n^{8/9})} on n-vertex graphs, and, if further the maximum degree is bounded, Existential Counting Modal Logic [Pilipczuk '11] can be model-checked in polynomial time. We also give a polynomial-time O(OPT²)-approximation for the stretch-width of symmetric 0,1-matrices or ordered graphs.
Somewhat unexpectedly, we prove that exponential subdivisions of bounded-degree graphs have bounded stretch-width. This allows to complement the logarithmic upper bound of treewidth with a matching lower bound. We leave as open the existence of an efficient approximation algorithm for the stretch-width of unordered graphs, if the exponential subdivisions of all graphs have bounded stretch-width, and if graphs of bounded stretch-width have logarithmic clique-width (or rank-width).
https://drops.dagstuhl.de/storage/00lipics/lipics-vol285-ipec2023/LIPIcs.IPEC.2023.8/LIPIcs.IPEC.2023.8.pdf
Contraction sequences
twin-width
clique-width
algorithms
algorithmic metatheorems