Dynamic Shortest Paths. Camil Demetrescu University of Rome “La Sapienza” Giuseppe F. Italiano University of Rome “Tor Vergata”. update weight of edge (u,v) to w. Update (u,v,w) :. return distance from x to y. Query (x,y) :. (or shortest path from x to y).
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
University of Rome “La Sapienza”
Giuseppe F. Italiano
University of Rome “Tor Vergata”
Update recomputingfrom scratch
O(n2.5 (C log n)0.5)
Henzinger et al. 97
O(n9/5 log13/5 n)
? < o(n3)
D, Italiano 01
O(n2.5 (S log3 n)0.5)
O(1)Previous work on fully dynamic APSP
The shortest path is different (update = decrease):
-Shortest paths and edge weight updates
How does a shortest path change after an update?
The combinatorial properties of uniform paths imply that only a small piece of information needs to be updated at each time…
Are we done?A new approach to dynamic APSP
A path is azombieif it used to be a shortest path,
and its edges have not been updated since then
O(zn2) zombies at any time
O(zn2) new potentially uniform paths per update
The combinatorial properties of potentially uniform paths imply that, if we do smoothing, we have only O(n2) new potentially uniform paths per update, amortized…A new approach to dynamic APSP (II)
There exists and updatealgorithm that spendsO(log n) time per potentially uniform path
Combinatorially well-behaved in dynamic graphs
New approach based on maintaining
potentially uniform paths
Applications to Railway Optimization Problems?
Solves the problem in its full generalityConclusions