2 research outputs found
Time-Dependent Shortest Path Queries Among Growing Discs
The determination of time-dependent collision-free shortest paths has
received a fair amount of attention. Here, we study the problem of computing a
time-dependent shortest path among growing discs which has been previously
studied for the instance where the departure times are fixed. We address a more
general setting: For two given points and , we wish to determine the
function which is the minimum arrival time at for any
departure time at . We present a -approximation algorithm
for computing . As part of preprocessing, we execute shortest path
computations for fixed departure times, where is the maximum
speed of the robot and is the minimum growth rate of the
discs. For any query departure time from , we can approximate the
minimum arrival time at the destination in time, within a factor of
of optimal. Since we treat the shortest path computations as
black-box functions, for different settings of growing discs, we can plug-in
different shortest path algorithms. Thus, the exact time complexity of our
algorithm is determined by the running time of the shortest path computations.Comment: 16 pages, 9 figures, abridged version submitted to CCCG 201