132 karma · joined October 26, 2012
Shortest-Path Queries in Static Networks http://www.sommer.jp/spq-survey.pdf
As a member of the Transit Routing team, you will work on one of the most anticipated features of Apple Maps. You will design and implement functionality that will be used by millions of users worldwide. Being part of a small team, you will have an influence on the future product. You will be responsible for implementing new features and resolving complex issues. You will work on high-performance server code using C++ in a Linux environment. Work with engineers and QA to deliver high-quality routes to our customers. Challenge the status quo and improve the design of existing software. Participate in design and code reviews.
[1] http://www.marketresearchworld.net/index.php?option=com_cont...
Mihai Patrascu, Mikkel Thorup: The Power of Simple Tabulation Hashing. J. ACM 59(3): 14 (2012) http://doi.acm.org/10.1145/2220357.2220361 (free version: http://arxiv.org/abs/1011.5200)
or also
Mihai Patrascu, Mikkel Thorup: Twisted Tabulation Hashing. SODA 2013: 209-228 http://knowledgecenter.siam.org/0236-000005/
If the graphs are grids (as in the cstheory.stackexchange.com question) they are planar and some dynamic data structures exist (unclear whether the constants are small enough for the application in question):
Exact shortest paths:
Jittat Fakcharoenphol, Satish Rao: Planar graphs, negative weight edges, shortest paths, and near linear time. J. Comput. Syst. Sci. 72(5): 868-889 (2006)
Approximate shortest paths:
Philip N. Klein, Sairam Subramanian: A Fully Dynamic Approximation Scheme for Shortest Paths in Planar Graphs. Algorithmica 22(3): 235-249 (1998)
Ittai Abraham, Shiri Chechik, Cyril Gavoille: Fully dynamic approximate distance oracles for planar graphs via forbidden-set distance labels. STOC 2012: 1199-1218