Fast and accurate estimation of shortest paths in large graphs
CIKM '10 Proceedings of the 19th ACM international conference on Information and knowledge management
Linear-space approximate distance oracles for planar, bounded-genus and minor-free graphs
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Distance oracles for vertex-labeled graphs
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
ESA'11 Proceedings of the 19th European conference on Algorithms
On approximate distance labels and routing schemes with affine stretch
DISC'11 Proceedings of the 25th international conference on Distributed computing
Exact distance oracles for planar graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Range selection and median: tight cell probe lower bounds and adaptive data structures
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Fast, precise and dynamic distance queries
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
A compact routing scheme and approximate distance oracle for power-law graphs
ACM Transactions on Algorithms (TALG)
Improved distance oracles and spanners for vertex-labeled graphs
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
The exact distance to destination in undirected world
The VLDB Journal — The International Journal on Very Large Data Bases
Brief announcement: a simple stretch 2 distance oracle
Proceedings of the 2013 ACM symposium on Principles of distributed computing
Shortest-path queries in static networks
ACM Computing Surveys (CSUR)
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Thorup and Zwick, in their seminal work, introduced the approximate distance oracle, which is a data structure that answers distance queries in a graph. For any integer k, they showed an efficient algorithm to construct an approximate distance oracle using space O(kn^{1+1/k}) that can answer queries in time O(k) with a distance estimate that is at most 2k-1 times larger than the actual shortest distance (this ratio is called the stretch).They proved that, under a combinatorial conjecture, their data structure is optimal in terms of space: if a stretch of at most 2k-1 is desired, then the space complexity is at least n^{1+1/k}. Their proof holds even if infinite query time is allowed: it is essentially an "incompressibility" result. Also, the proof only holds for dense graphs, and the best bound it can prove only implies that the size of the data structure is lower bounded by the number of edges of the graph. Naturally, the following question arises: what happens for sparse graphs? In this paper we give a new lower bound for approximate distance oracles in the cell-probe model. This lower bound holds even for sparse (polylog(n)-degree) graphs, and it is not an "incompressibility" bound: we prove a three-way tradeoff between space, stretch, and query time. We show that when the query time is t and the stretch is a, then the space S must be at least n^{1+1/Omega(a*t)} / lg n. This lower bound follows by a reduction from lopsided set disjointness to distance oracles, based on and motivated by recent work of Patrascu. Our results in fact show that for any high-girth regular graph, an approximate distance oracle that supports efficient queries for all subgraphs of G must obey this tradeoff. We also prove some lemmas that count sets of paths in high-girth regular graphs and high-girth regular expanders, which might be of independent interest.