Faster and enhanced inclusion-minimal cograph completion

We design two incremental algorithms for computing an inclusion-minimal completion of arbitrary graph into a cograph. The first one is able to do so while providing additional property which crucial in practice obtain completions using as few edges possible : it compute minimum-cardinality the neighbourhood new vertex introduced at each step. It runs O(n+m′) time, where m′ number completed graph. This matches complexity algorithm (Lokshtanov et al., 2010) and positively answers their open questions. Our second improves O(n+mlog2n) when above not required. Moreover, we prove that many very sparse graphs, having only O(n) edges, require Ω(n2) any cograph completions. For these include those encountered applications, improvement on scales O(n∕log2n).