We revisit the problem of computing shortest obstacle-avoiding paths among obstacles in three dimensions. We prove new hardness results, showing, e.g., that computing Euclidean sh...
We study the problem of finding small weak -nets in three dimensions and provide new upper and lower bounds on the value of for which a weak -net of a given small constant size e...
Let B be a set of n unit balls in R3 . We show that the combinatorial complexity of the space of lines in R3 that avoid all the balls of B is O(n3+ε ), for any ε > 0. This re...
Pankaj K. Agarwal, Boris Aronov, Vladlen Koltun, M...
In orthogonal range reporting we are to preprocess N points in d-dimensional space so that the points inside a d-dimensional axis-aligned query box can be reported efficiently. T...
This paper presents a new framework for drawing graphs in three dimensions. In general, the new framework uses a divide and conquer approach. More specifically, the framework divi...