The contiguous art gallery problem is solvable in O(k n^2 log^2 n) time using O(n^2) candidate greedy start points and an O(log^2 n)-time farthest-visible-chain query.
Linear time algorithms for visibility and shortest path problems inside simple polygons
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Simpler and Faster Contiguous Art Gallery
The contiguous art gallery problem is solvable in O(k n^2 log^2 n) time using O(n^2) candidate greedy start points and an O(log^2 n)-time farthest-visible-chain query.