Additive sparse spanners for graphs with bounded length of largest induced cycle

Theoretical Computer Science

Volumn 347, Issue 1-2, 2005, Pages 54-75

  Chepoi, Victor D ^a   Dragan, Feodor F ^b   Yan, Chenyu ^b  

^a AIX MARSEILLE UNIVERSITY   (France)

^b KENT STATE UNIVERSITY   (United States)

Author keywords

Additive graph spanners; Distance; Efficient algorithms; k chordal graphs

Indexed keywords

GRAPH THEORY; MATHEMATICAL MODELS;

ADDITIVE SPARSE SPANNERS; BONDED LENGTH;

COMPUTER SCIENCE;

EID: 27844601148     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2005.05.017     Document Type: Article

References (32)

1. I. Althöfer, G. Das, D. Dobkin, D. Joseph, and J. Soares On sparse spanners of weighted graphs Discrete Comput. Geom. 9 1993 81 100
2. H.-J. Bandelt, and A. Dress Reconstructing the shape of a tree from observed dissimilarity data Adv. Appl. Math. 7 1986 309 343
3. U. Brandes, D. Handke, NP-completeness results for minimum planar spanners, University of Konstanz, Konstanzer Schriften in Mathematik und Informatik, Nr. 16, Preprint, Oktober 1996.
4. A. Brandstädt, V. Chepoi, and F. Dragan Distance approximating trees for chordal and dually chordal graphs J. Algorithms 30 1999 166 184
5. A. Brandstädt, F. Dragan, V. Chepoi, and V. Voloshin Dually chordal graphs SIAM J. Discrete Math. 11 1998 437 455
6. A. Brandstädt, F.F. Dragan, H.-O. Le, V.B. Le, Tree spanners on chordal graphs: complexity, algorithms, open problems, Proc. 13th Internat. Symp. on Algorithms and Computation (ISAAC'02), November 2002, Lecture Notes in Computer Science, Vol. 2518, Springer, Berlin, pp. 163-174.
7. A.E. Brouwer, P. Duchet, and A. Schrijver Graphs whose neighbourhoods have no special cycles Discrete Math. 47 1983 177 182
8. L. Cai, Tree spanners: spanning trees that approximate the distances, Ph.D. Thesis, University of Toronto, 1992.
9. L. Cai, and D.G. Corneil Tree spanners SIAM J. Discrete Math. 8 1995 359 387
10. V. Chepoi, and F. Dragan A note on distance approximating trees in graphs European J. Combin. 21 2000 761 766
11. F.F. Dragan, Estimating all pairs shortest paths in restricted graph families: a unified approach (extended abstract), Proc. 27th Internat. Workshop "Graph-Theoretic Concepts in Computer Science" (WG'01), June 2001, Lecture Notes in Computer Science, Vol. 2204, Springer, Berlin, pp. 103-116.
12. F.F. Dragan, and V. Voloshin Incidence graphs of biacyclic hypergraphs Discrete Appl. Math. 68 1996 259 266
13. M. Farber Characterizations of strongly chordal graphs Discrete Math. 43 1983 173 189
14. S.P. Fekete, and J. Kremer Tree spanners in planar graphs Discrete Appl. Math. 108 2001 85 103
15. J.R. Gilbert, D.J. Rose, and A. Edenbrandt A separator theorem for chordal graphs SIAM J. Algebraic Discrete Methods 5 1984 306 313
16. M.C. Golumbic Algorithmic Graph Theory and Perfect Graphs 1980 Academic Press New York
17. Hoàng-Oanh Le, Effiziente Algorithmen für Baumspanner in chordalen Graphen, Diploma Thesis, Department of Mathematics, Technical University of Berlin, 1994.
18. H.-O. Le, and V.B. Le Optimal tree 3-spanners in directed path graphs Networks 34 1999 81 87
19. A.L. Liestman, and T. Shermer Additive graph spanners Networks 23 1993 343 364
20. A. Lubiw Doubly lexical orderings of matrices SIAM J. Comput. 16 1987 854 879
21. M.S. Madanlal, G. Venkatesan, and C. Pandu Rangan Tree 3-spanners on interval, permutation and regular bipartite graphs Inform. Process. Lett. 59 1996 97 102
22. I.E. Papoutsakis, Two structure theorems on tree spanners, M.Sc. Thesis, Department of Computer Science, University of Toronto, 1999.
23. I.E. Papoutsakis, On the union of two tree spanners of a graph, Manuscript, 2001.
24. D. Peleg Distributed Computing: A Locality-Sensitive Approach, SIAM Monographs on Discrete Mathematical Applications 2000 SIAM Philadelphia
25. D. Peleg, and A.A. Schäffer Graph spanners J. Graph Theory 13 1989 99 116
26. D. Peleg, and J.D. Ullman An optimal synchronizer for the hypercube Proc. Sixth ACM Symp. on Principles of Distributed Computing Vancouver 1987 77 85
27. D. Peleg, and E. Upfal A tradeoff between space and efficiency for routing tables 20th ACM Symp. on the Theory of Computing Chicago 1988 43 52
28. E. Prisner, Distance approximating spanning trees, in: R. Reischuk, M. Morvan (Eds.), Proc. of STACS'97, Lecture Notes in Computer Science, Vol. 1200, Springer, Berlin, New York, 1997, pp. 499-510.
29. E. Prisner, D. Kratsch, H.-O. Le, H. Müller, and D. Wagner Additive tree spanners SIAM J. Discrete Math. 17 2003 332 340
30. J. Soares Graph spanners: a survey Congr. Numer. 89 1992 225 238
31. J.P. Spinrad Doubly lexical ordering of dense 0-1-matrices Inform. Process. Lett. 45 1993 229 235
32. G. Venkatesan, U. Rotics, M.S. Madanlal, J.A. Makowsky, and C. Pandu Ragan Restrictions of minimum spanner problems Inform. Comput. 136 1997 143 164