Rectilinear path problems in restricted memory setup

The objective of the Path-Query (p,q) in the in-place setup is to preprocess the input rectangles in a data structure in the input array itself such that for any pair of query points p and q, a rectilinear path can be reported efficiently. Here we propose an algorithm with O(nlogn) preprocessing time and O(n3/4+χ) query time, where χ is the number of links (bends) in the path. Both the preprocessing and query answering need O(1) extra space.