On sparse spanners of weighted graphs
Discrete & Computational Geometry
Fast Estimation of Diameter and Shortest Paths (Without Matrix Multiplication)
SIAM Journal on Computing
Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
$(1 + \epsilon,\beta)$-Spanner Constructions for General Graphs
SIAM Journal on Computing
Journal of the ACM (JACM)
Computing almost shortest paths
ACM Transactions on Algorithms (TALG)
Spanners and emulators with sublinear distance errors
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Ramsey partitions and proximity data structures
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Lower Bounds for Additive Spanners, Emulators, and More
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Compact name-independent routing with minimum stretch
ACM Transactions on Algorithms (TALG)
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
Distance Oracles for Sparse Graphs
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Additive spanners and (α, β)-spanners
ACM Transactions on Algorithms (TALG)
Distance Oracles beyond the Thorup-Zwick Bound
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Sparse spanners vs. compact routing
Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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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For every integral parameter k 1, given an unweighted graph G, we construct in polynomial time, for each vertex u, a distance label L(u) of size Õ(n2/(2k-1)). For any u, v ε G, given L(u), L(v) we can return in time O(k) an affine approximation d(u, v) on the distance d(u, v) between u and v in G such that d(u, v) ≤ d(u, v) ≤ (2k - 2)d(u, v) + 1. Hence we say that our distance label scheme has affine stretch of (2k - 2)d + 1. For k = 2 our construction is comparable to the O(n5/3) size, 2d + 1 affine stretch of the distance oracle of Pătrascu and Roditty (FOCS '10), it incurs a o(log n) storage overhead while providing the benefits of a distance label. For any k 1, given a restriction of o(n1+1/(k-1)) on the total size of the data structure, our construction provides distance labels with affine stretch of (2k - 2)d+1 which is better than the stretch (2k - 1)d scheme of Thorup and Zwick (J. ACM '05). Our second contribution is a compact routing scheme with poly-logarithmic addresses that provides affine stretch guarantees. With Õ(n3/(3k-2))-bit routing tables we obtain affine stretch of (4k - 6)d+1, for any k 1. Given a restriction of o(n1/(k-1)) on the table size, our routing scheme provides affine stretch which is better than the stretch (4k - 5)d routing scheme of Thorup and Zwick (SPAA '01).