Approximate distance oracles for unweighted graphs in expected O(n 2) time

ACM Transactions on Algorithms

Volumn 2, Issue 4, 2006, Pages 557-577

  Baswana, Surender ^a   Sen, Sandeep ^b  

^a MAX PLANCK INSTITUTE FOR INFORMATICS   (Germany)

^b INDIAN INSTITUTE OF TECHNOLOGY DELHI   (India)

Author keywords

Approximate distance oracles; Distance queries; Distances; Shortest paths; Spanners

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTATION THEORY; DATA STRUCTURES; INTEGER PROGRAMMING; QUADRATIC PROGRAMMING; QUERY LANGUAGES;

APPROXIMATE DISTANCE ORACLES; DISTANCE QUERIES; SUBQUADRATIC SPACE; UNWEIGHTED GRAPH;

GRAPH THEORY;

EID: 33846593294     PISSN: 15496325     EISSN: 15496333     Source Type: Journal    
DOI: 10.1145/1198513.1198518     Document Type: Conference Paper

References (16)

1. AINGWORTH, D., CHEKURI, C., INDYK, P., AND MOTWANI, R. 1999. Fast estimation of diameter and shortest paths(without matrix multiplication). SIAM J. Comput. 28, 1167-1181.
2. AWERBUCH, B., BERGER, B., COWEN, L., AND PELEG, D. 1998. Near-linear time construction of sparse neighborhod covers. SIAM J. Comput. 28, 263-277.
3. 2polylog n) time. In Proceedings of 22nd Annual Symposium on Theoretical Aspect of Computer Science. Lecture Notes in Computer Science, vol. 3404. Springer-Verlag, New York, 666-679.
4. 1+1/k) size in weighted graphs. In Proceedings of the 30th International Colloquium on Automata, Languages and Programming. Lecture Notes in Computer Science, vol. 2719. Springer-Verlag, New York, 384-396.
5. BASWANA, S., TELIKEPALLI, K., MEHLHORN, K., AND PETTIE, S. 2005b. New construction of (α, β)-spanners and purely additive spanners. In Proceedings of 16th Annual ACM-SIAM Symposium on Discrete Algorithms (Vancouver, BC, Canada). ACM, New York, 672-681.
6. 3/ log n) time. In Proceedings of Workshop on Algorithms and Data Structures. Lecture Notes in Computer Science, vol. 3608. Springer-Verlag, New York, 318-324.
7. OHEN, E. 1998. Fast algorithms for constructing t-spanners and paths with stretch t. SIAM J. Comput. 28, 210-236.
8. OHEN, E., AND ZWICK, U. 2001. All-pairs small stretch paths. J. Algor. 38, 335-353.
9. OR, D., HALPERIN, S., AND ZWICK, U. 2000. All pairs almost shortest paths. SIAM J. Comput. 29, 1740-1759.
10. ELKIN, M. 2005. Computing almost shortest paths. ACM Trans. Algor. 1, 282-323.
11. ERDÖS, P. 1964. Extremal problems in graph theory. In Theory of Graphs and its Applications (Proc. Sympos. Smolenice, 1963). Publ. House Czechoslovak Acad. Sci., Prague, 29-36.
12. FREDMAN, M. L., KOMLÓS, J., AND SZEMERÉDI, E. 1984. Storing a sparse table with O(1) worst case time. JACM 31, 53 8-544.
13. HALPERIN, S. AND ZWICK, U. 1996. Linear time deterministic algorithm for computing spanners for unweighted graphs, unpublished manuscript.
14. PETTIE, S. 2004. A new approach to all-pairs shortest paths on real-weighted graphs. Theoret. Comput. Sci. 312, 47-74.
15. RODITTY, L., THORUP, M., AND ZWICK, U. 2005. Deterministic construction of approximate distance oracles and spanners. In Proceedings of 32nd International Colloquim on Automata, Languagaes and Programming. Lecture Notes in Computer Science, vol. 3580. Springer-Verlag, New York, 261-272.
16. THORUP, M. AND ZWICK, U. 2005. Approximate distance oracles. JACM 52, 1-24.