  An orientation of a grid is called unique sink orientation (USO) if each of
its nonempty subgrids has a unique sink. Particularly, the original grid itself
has a unique global sink. In this work we investigate the problem of how to
find the global sink using minimum number of queries to an oracle. There are
two different oracle models: the vertex query model where the orientation of
all edges incident to the queried vertex are provided, and the edge query model
where the orientation of the queried edge is provided. In the 2-dimensional
case, we design an optimal linear deterministic algorithm for the vertex query
model and an almost linear deterministic algorithm for the edge query model,
previously the best known algorithms run in O(N logN) time for the vertex query
model and O(N^1.404) time for the edge query model.
