A Lower Bound for the Query Phase of Contraction Hierarchies and Hub Labels and a Provably Optimal Instance-Based Schema
Keyword(s):
Speed Up
◽
We prove a Ω(n) lower bound on the query time for contraction hierarchies (CH) as well as hub labels, two popular speed-up techniques for shortest path routing. Our construction is based on a graph family not too far from subgraphs that occur in real-world road networks, in particular, it is planar and has a bounded degree. Additionally, we borrow ideas from our lower bound proof to come up with instance-based lower bounds for concrete road network instances of moderate size, reaching up to 96% of an upper bound given by a constructed CH. For a variant of our instance-based schema applied to some special graph classes, we can even show matching upper and lower bounds.
Keyword(s):
2017 ◽
Vol 7
(2)
◽
pp. 169-181
Keyword(s):
2014 ◽
Vol 25
(07)
◽
pp. 877-896
◽
Keyword(s):
2010 ◽
Vol 02
(03)
◽
pp. 363-377
◽
Keyword(s):
2011 ◽
Vol 12
(01n02)
◽
pp. 1-17
◽
Keyword(s):
1987 ◽
Vol 17
(10)
◽
pp. 1309-1311
◽
Keyword(s):
2018 ◽
Vol 29
(04)
◽
pp. 551-569
◽