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Communication Dans Un Congrès Année : 2023

Stretch-width

Résumé

We introduce a new parameter, called stretch-width, that we show sits strictly between cliquewidth 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 4/5) 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(OPT 2)-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).
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Dates et versions

hal-04292981 , version 1 (17-11-2023)

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  • HAL Id : hal-04292981 , version 1

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Édouard Bonnet, Julien Duron. Stretch-width. IPEC 2023, Sep 2023, Amsterdam, Netherlands. ⟨hal-04292981⟩
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