SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Compact routing with minimum stretch
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Compact roundtrip routing for digraphs
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Compact roundtrip routing in directed networks (extended abstract)
Proceedings of the nineteenth annual ACM symposium on Principles of distributed computing
Approximating k-Spanner Problems for k2
Proceedings of the 8th International IPCO Conference on Integer Programming and Combinatorial Optimization
On the Power of BFS to Determine a Graphs Diameter
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
Estimating All Pairs Shortest Paths in Restricted Graph Families: A Unified Approach
WG '01 Proceedings of the 27th International Workshop on Graph-Theoretic Concepts in Computer Science
All Pairs Shortest Paths in Undirected Graphs with Integer Weights
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Compact roundtrip routing with topology-independent node names
Proceedings of the twenty-second annual symposium on Principles of distributed computing
Compact roundtrip routing in directed networks
Journal of Algorithms
Approximating Minimum Max-Stretch spanning Trees on unweighted graphs
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Sparse source-wise and pair-wise distance preservers
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Approximating k-spanner problems for k 2
Theoretical Computer Science
Estimating all pairs shortest paths in restricted graph families: a unified approach
Journal of Algorithms
Compact roundtrip routing with topology-independent node names
Journal of Computer and System Sciences
Estimating all pairs shortest paths in restricted graph families: a unified approach
Journal of Algorithms
Indexing Network Structure with Shortest-Path Trees
ACM Transactions on Knowledge Discovery from Data (TKDD)
Exact distance labelings yield additive-stretch compact routing schemes
DISC'06 Proceedings of the 20th international conference on Distributed Computing
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Let G=(V,E) be an unweighted undirected graph on n vertices. A simple argument shows that computing all distances in G with an additive one-sided error of at most 1 is as hard as Boolean matrix multiplication. Building on recent work of D. Aingworth et al. (1996), we describe an O/spl tilde/(min{n/sup 3/2/m/sup 1/2/,n/sup 7/3/}) time algorithm APASP/sub 2/ for computing all distances in G with an additive one-sided error of at most 2. The algorithm APASP/sub 2/ is simple, easy to implement, and faster than the fastest known matrix multiplication algorithm. Furthermore, for every even k2, we describe an O/spl tilde/(min{n/sup 2-(2)/(k+2)/m/sup (2)/(k+2)/, n/sup 2+(2)/(3k-2)/}) time algorithm APASP/sub k/ for computing all distances in G with an additive one-sided error of at most k. We also give an O/spl tilde/(n/sup 2/) time algorithm APASP/sub /spl infin// for producing stretch 3 estimated distances in an unweighted and undirected graph on n vertices. No constant stretch factor was previously achieved in O/spl tilde/(n/sup 2/) time. We say that a weighted graph F=(V,E') k-emulates an unweighted graph G=(V,E) if for every u, v/spl isin/V we have /spl delta//sub G/(u,v)/spl les//spl delta//sub F/(u,v)/spl les//spl delta//sub G/(u,v)+k. We show that every unweighted graph on n vertices has a 2-emulator with O/spl tilde/(n/sup 3/2/) edges and a 4-emulator with O/spl tilde/(n/sup 4/3/) edges. These results are asymptotically tight. Finally, we show that any weighted undirected graph on n vertices has a 3-spanner with O/spl tilde/(n/sup 3/2/) edges and that such a 3-spanner can be built in O/spl tilde/(mn/sup 1/2/) time. We also describe an O/spl tilde/(n(m/sup 2/3/+n)) time algorithm for estimating all distances in a weighted undirected graph on n vertices with a stretch factor of at most 3.