How to make a square grid framework with cables rigid

SIAM Journal on Computing

Volumn 30, Issue 2, 2000, Pages 649-680

  Gabow, Harold N ^a   Jordán, Tibor ^b  

^a University of Colorado at Boulder   (United States)

^b AARHUS UNIVERSITY   (Denmark)

Author keywords

Connectivity augmentation; Graph algorithms; Min max theorems; Rigidity; Square grid framework; Strong connectivity

Indexed keywords

ALGORITHMS; CABLES; CONSTRAINT THEORY; GRAPH THEORY; PROBLEM SOLVING; RIGIDITY; STRUCTURAL ANALYSIS;

CONNECTIVITY AUGMENTATION; SQUARE GRID FRAMEWORKS;

STRUCTURAL FRAMES;

EID: 0041946100     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0097539798347189     Document Type: Article

References (16)

1. J.A. BAGLIVO AND J.E. GRAVER, Incidence and Symmetry in Design and Architecture, Cambridge University Press, Cambridge, UK, 1983.
2. J. BANG-JENSEN AND T. JORDÁN, Edge-connectivity augmentation preserving simplicity, SIAM J. Discrete Math., 11 (1998), pp. 603-623.
3. J. BANG-JENSEN, H.N. GABOW, T. JORDÁN, AND Z. SZIGETI, Edge-connectivity augmentation with partition constraints, SIAM J. Discrete Math., 12 (1999), pp. 160-207.
4. E.D. BOLKER AND H. CRAPO, How to brace a one-story building, Environ. Plan. B, 4 (1977), pp. 125-152.
5. T.H. CORMEN, C.E. LEISERSON, AND R.L. RIVEST, Introduction to Algorithms, McGraw-Hill, New York, 1990.
6. K.P. ESWARAN AND R.E. TARJAN, Augmentation problems, SIAM J. Comput., 5 (1976), pp. 653-665.
7. A. FRANK, Connectivity augmentation problems in network design, in Mathematical Programming: State of the Art 1994, J.R. Birge and K.G. Murty, eds., University of Michigan, Ann Arbor, MI, 1994, pp. 34-63.
8. H. N. GABOW AND T. JORDÁN, Bipartition constrained edge-splitting in directed graphs, in Proceedings of the 1st Japanese-Hungarian Symp. on Discrete Math, and its Applications, Kyoto, Japan, 1999, pp. 225-232.
9. M. GRÖTSCHEL, C.L. MONMA, AND M. STOER, Design of survivable networks, in Handbook in Operations Research and Management Science, M.O. Ball, T.L. Magnanti, C.L. Monma, and G.L. Nemhauser, eds., Network Models 7, North-Holland, Amsterdam, The Netherlands, 1994, pp. 617-672.
10. T-S. HSU AND M-Y. KAO, Optimal augmentation for bipartite componentwise biconnectivity in linear time, in Algorithms and Computation (Proc. ISAAC '96), Lecture Notes in Comput. Sci. 1178, Springer-Verlag, New York, 1996, pp. 213-222.
11. T. ISHII, H. NAGAMOCHI, AND T. IBARAKI, Optimal augmentation to make a graph k-edge-connected and triconnected, in Proceedings of the 9th Annual ACM-SIAM Symp. on Discrete Algorithms, ACM, New York, 1998, pp. 280-289.
12. T. JORDAN, Two NP-Complete Augmentation Problems, Preprint 8, Department of Mathematics and Computer Science, Odense University, 1997.
13. G. KANT AND H.L. BODLAENDER, Planar graph augmentation problems, in Algorithms and Data Structures (Proc. WADS '91), Lecture Notes in Comput. Sci. 519, Springer-Verlag, New York, 1991, pp. 286-298.
14. H. NAGAMOCHI AND P. EADES, Edge-splitting and edge-connectivity augmentation in planar graphs, in Integer Programming and Combinatorial Optimization, Lecture Notes in Comput. Sci. 1412, Springer-Verlag, New York, 1998, pp. 96-111.
15. A. RECSKI, Matroid Theory and its Applications in Electric Network Theory and in Statics, Akadémiai Kiadó, Budapest, 1989.
16. M. STOER, Design of Survivable Networks, Lecture Notes in Math. 1531, Springer-Verlag, New York, 1992.