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
Multiplicative approximations of random walk transition probabilities
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
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
Approximate distance oracles with improved preprocessing time
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Exact distance oracles for planar graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Two-Dimensional range diameter queries
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
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
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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We give the first improvement to the space/approximation trade-off of distance oracles since the seminal result of Thorup and Zwick [STOC'01]. For unweighted graphs, our distance oracle has size $O(n^{5/3}) = O(n^{1.66\cdots})$ and, when queried about vertices at distance $d$, returns a path of length $2d+1$. For weighted graphs with $m=n^2/\alpha$ edges, our distance oracle has size $O(n^2 / \sqrt[3]{\alpha})$ and returns a factor 2 approximation. Based on a plausible conjecture about the hardness of set intersection queries, we show that a 2-approximate distance oracle requires space $\tOmega(n^2 / \sqrt{\alpha})$. For unweighted graphs, this implies a $\tOmega(n^{1.5})$ space lower bound to achieve approximation $2d+1$.