Approximation metatheorem for fractionally treewidth-fragile graphs

03/15/2021

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by   Zdeněk Dvořák, et al.

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Baker's technique is a powerful tool for designing polynomial-time approximation schemes, in particular for all optimization problems expressible in monotone first-order logic. However, it can only be used in rather restricted graph classes. We show that maximization problems expressible in monotone first-order logic admit PTAS under a much weaker assumption of fractional treewidth-fragility, and QPTAS on all hereditary classes with sublinear separators.