Conditional lower bound rules out O(n^{2-ε}) algorithms for isometric/convex subgraph testing on sparse graphs; subquadratic time for planar graphs and near-linear time for bounded-treewidth and certain plane graphs.
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Testing whether a subgraph is convex or isometric
Conditional lower bound rules out O(n^{2-ε}) algorithms for isometric/convex subgraph testing on sparse graphs; subquadratic time for planar graphs and near-linear time for bounded-treewidth and certain plane graphs.