Tree spanners in planar graphs

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1517, Issue , 1998, Pages 298-309

  Fekete, Sándor P ^a   Kremer, Jana ^b  

^a UNIVERSITY OF COLOGNE   (Germany)

^b UNIVERSITY OF BAMBERG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

GRAPHIC METHODS; POLYNOMIAL APPROXIMATION;

GRAPH G; NP-HARD; PLANAR GRAPH; POLYNOMIAL ALGORITHM; POLYNOMIAL-TIME; SUB TREES; TREE T-SPANNER; UNWEIGHTED GRAPHS;

TREES (MATHEMATICS);

EID: 22444456008     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/10692760_24     Document Type: Conference Paper

References (23)

1. I. Althofer, G. Das, D. Dobkin, D. Joseph, and J. Soares. On sparse spanners of weighted graphs. Discrete and Computational Geometry, 9 (1993), pp. 81-100.
2. S. Arikati, D. Z. Chen, L. P. Chew, G. Das, M. Smid, and D. Zaroliagis. Planar spanners and approximate shortest path queries among obstacles in the plane.. In: J. Diaz, ed., Algorithms - ESA '96, Springer Lecture Notes in Computer Science #1136, 1996, pp. 514-528.
3. B. Awerbuch, A. Baratz, and D. Peleg. Efficient broadcast and light-weight spanners. Manuscript, 1992.
4. S. Bhatt, F. Chung, F. Leighton, and A. Rosenberg. Optimal simulations of tree machines. In Proceedings of the 27th IEEE Symposium on Foundations of Computer Science (FOCS 1986), pp. 274-282.
5. J. A. Bondy and U. S. R. Murty. Graph Theory with Applications. North-Holland, New York, 1976.
6. K. S. Booth and G. S. Lueker. Testing for the consecutive ones property, interval graphs, and planarity using PQ-tree algorithms. Journal of Computer and System Sciences, 13 (1976), pp. 335-379.
7. U. Brandes and D. Handke. NP-completeness results for minimum planar spanners. In Proceedings of the 23th Workshop on Graph-Theoretic Concepts in Computer Science (WG '97), Springer Lecture Notes in Computer Science # 1335, 1997, pp. 85-99.
8. L. Cai. Tree spanners: spanning trees that approximate distances. Ph. D. thesis, University of Toronto, Toronto, Canada, 1992. Available as Technical Report 260/92, Department of Computer Science, University of Toronto.
9. L. Cai. NP-completeness of minimum spanner problems, Discrete Applied Mathematics, 48 (1994), pp. 187-194.
10. L. Cai and D. G. Corneil. Tree spanners. SIAM Journal ofDiscrete Mathematics, 8 (1995), pp. 359-387.
11. L. P. Chew. There is a planar graph almost as good as the complete graph. In Proceedings of the 2nd ACM Symposium on Computational Geometry, pp. 169177, 1986.
12. D. P. Dobkin, S. J. Friedman, and K. J. Supowit. Delaunay graphs are almost as good as complete graphs. Discrete and Computational Geometry, 5 (1990), pp. 399407.
13. J. E. Hopcroft and R. E. Tarjan. Efficient planarity testing. Journal of the ACM, 21, (1974), 549-568.
14. G. Kortsarz and D. Peleg. Generating sparse 2-spanners. In: Proceedings of the Third Scandinavian Workshop on Algorithm Theory (SWAT 1992).
15. J. Kremer. Baumspanner in planaren Graphen. Diploma thesis, Mathematisches Institut, Universitat zu Koln, 1997.
16. D. Lichtenstein. Planar formulae and their uses. SIAM Journal ofComputing, 11 (1982), pp. 329-343.
17. A. L. Liestman and T. Shermer. Grid spanners. Networks, 23 (1993), pp. 123-133.
18. A. Mansfield. Determining the thickness of graphs is NP-hard. Mathematical Proceedings ofthe Cambridge Philosophical Society, 93 (1983), pp. 9-23.
19. D. Peleg and A. A. Schaffer. Graph spanners. Journal of Graph Theory, 13 (1989), pp. 99-116.
20. D. Peleg and J. D. Ullman. An optimal synchronizer for the hypercube. In Proceedings of the 6th ACM Symposium on Principles of Distributed Computing, 1987, pp. 77-85.
21. D. Peleg and E. Upfal. A tradeoff between space and efficiency for routing tables. In Proceedings ofthe 20th ACM Symposium on the Theory ofComputing, (STOC 1988), pp. 43-52.
22. D. Richards and A. L. Liestman. Degree-constrained pyramid spanners. Parallel and Distributed Computing, 25 (1995), pp. 1-6.
23. J. Soares. Graph spanners: a survey. Congressus Numerantium, 89 (1992),pp. 225-238.