Before revision:  Given that biclique edge-partition, we show how to solve the unweighted Single-Source Shortest Paths and hence All-Pairs Shortest Paths in sublinear time O(n \log n) and time O(n^2 \log n), respectively  .
After revision:  Given that biclique edge-partition, we show how to solve the unweighted Single-Source Shortest Paths and hence All-Pairs Shortest Paths in sublinear time O(n \log n) and time O(n^2 \log n), respectively . Finally we show that Min Dominating Set and related problems have constant integrality gaps on bounded twin-width classes, thereby getting constant approximations on these classes .