Applications of parameterized St-Orientations

Journal of Graph Algorithms and Applications

Volumn 14, Issue 2, 2010, Pages 337-365

  Papamanthou, Charalampos ^a   Tollis, Ioannis G ^b  

^a BROWN UNIVERSITY   (United States)

^b UNIVERSITY OF CRETE   (Greece)

Author keywords

[No Author keywords available]

Indexed keywords

CLUSTERING ALGORITHMS; DIRECTED GRAPHS; DRAWING (GRAPHICS);

GRAPH DRAWING ALGORITHMS; GRAPH G; LINEAR-TIME ALGORITHMS; LONGEST PATH; PARAMETERIZED; PATHLENGTHS; SINGLE SOURCE; SPACE SAVINGS; UNDIRECTED GRAPH; VISIBILITY REPRESENTATION;

UNDIRECTED GRAPHS;

EID: 84455176866     PISSN: 15261719     EISSN: None     Source Type: Journal    
DOI: 10.7155/jgaa.00210     Document Type: Article

References (29)

1. M. M. Akon, S. Asaduzzaman, M. S. Rahman, and M. Matsumoto. Pro-posal for st-routing. Telecommunication Systems, 25(3-4):287-298, 2004.
2. F. Annexstein and K. Berman. Directional routing via generalized st-numberings. SIAM Journal on Discrete Mathematics, 13(2):268-279, 2000.
3. U. Brandes. Eager st-ordering. In Proc. European Symposium on Algorithms (ESA), pages 247-256, 2002.
4. H. de Fraysseix, P. de Mendez, and P. Rosenstiehl. Bipolar orientations revisited. Discrete Applied Mathematics, 56:157-179, 1995.
5. G. Di Battista, P. Eades, R. Tamassia, and I. G. Tollis. Graph Drawing: Algorithms for the Visualization of Graphs. Prentice Hall, 1999.
6. J. Ebert. st-ordering the nodes of biconnected graphs. Computing, 30(1):19-33, 1983.
7. S. Even and R. Tarjan. Computing an st-numbering. Theoretical Computer Science, 2:339-344, 1976.
8. T. Gallai. On directed paths and circuits. In Proc. Theory of Graphs: International Symposium, pages 215-232, 1967.
9. M. Garey and D. Johnson. Computers and intractability: A guide to the theory of NP-completeness. W. H. Freeman and Company, 1979.
10. M. T. Goodrich and R. Tamassia. Data structures and algorithms in JAVA. John Wiley & Sons, 2005.
11. X. He and H. Zhang. Nearly optimal visibility representations of plane graphs. In Proc. Colloquium on Automata, Languages and Programming (ICALP), pages 407-418, 2006.
12. J. Holm, K. de Lichtenberg, and M. Thorup. Poly-logarithmic deterministic fully-dynamic algorithms for connectivity, minimum spanning tree, 2-edge and biconnectivity. Journal of the ACM, 48(4):723-760, 2001.
13. J. Hopcroft and R. Tarjan. Effcient algorithms for graph manipulation. Communications of the ACM, 16:372-378, 1973.
14. A. Lempel, S. Even, and I. Cederbaum. An algorithm for planarity testing of graphs. In Proc. Theory of Graphs: International Symposium, pages 215-232, 1967.
15. T. Lukovszki and W.-B. Strothmann. Decremental biconnectivity on planar graphs. Technical report TR-RI-97-186, University of Paderborn, 1997.
16. Y. Maon, B. Schieber, and U. Vishkin. Parallel ear decomposition search (EDS) and st-numbering in graphs. Theoretical Computer Science, 47:277-298, 1986.
17. A. Papakostas and I. G. Tollis. Algorithms for area-effcient orthogonal drawings. Computational Geometry: Theory and Applications, 9:83-110, 1998.
18. A. Papakostas and I. G. Tollis. Effcient orthogonal drawings of high degree graphs. Algorithmica, 26(1):100-125, 2000.
19. C. Papamanthou and I. G. Tollis. Algorithms for computing a parameter-ized st-orientation. Theoretical Computer Science, 408:224-240, 2008.
20. P. Rosenstiehl and R. Tarjan. Rectilinear planar layout and bipolar orien-tation of planar graphs. Discrete and Computational Geometry, 1:343-353, 1986.
21. S. Sadasivam and H. Zhang. NP-completeness of st-orientations for plane graphs. In Proc. Fundamentals of Computation Theory (FCT), pages 298-309, 2009.
22. G. Schaeffer. Bijective census and random generation of eulerian planar maps with prescribed degrees. Electronic Journal of Combinatorics, 4(1), 1997.
23. R. Tamassia and I. G. Tollis. A uniffed approach to visibility representations of planar graphs. Discrete and Computational Geometry, 1:321-341, 1986.
24. R. Tarjan. Two streamlined depth-first search algorithms. Fundamenta Informaticae, 9:85-94, 1986.
25. L. Vitaver. Determination of minimal coloring of vertices of a graph by means of boolean powers of the incidence matrix. Dokl. Akad. Nauk. SSSR., 147:758-759, 1962.
26. H. Zhang and X. He. On visibility representation of plane graphs. In Proc. Symposium on Theoretical Aspects of Computer Science (STACS), pages 477-488, 2004.
27. H. Zhang and X. He. Improved visibility representation of plane graphs. Computational Geometry, 30(1):29-39, 2005.
28. H. Zhang and X. He. Visibility representation of plane graphs via canonical ordering tree. Information Processing Letters, 96(2):41-48, 2005.
29. H. Zhang and X. He. Optimal st-orientations for plane triangulations. Journal of Combinatorial Optimization, 17(4):367-377, 2009.