Computational Topology

• On computing handle and tunnel loops T. K. Dey, K. Li, and  J. Sun.  IEEE Proc. NASAGEM 07, to appear. Tech Report OSU-CISRC-06/07-TR48, June 2007.
• Delaunay refinement for piecewise smooth complexes
  S.-W. Cheng, T. K. Dey, and E. A. Ramos. Proc. 18th Annu. ACM-SIAM Sympos. Discrete Algorithms (2007), 1096--1105.
  

• Stability of critical points with interval persistence T. K. Dey and R. Wenger.  Discrete & Computational Geometry, to appear. Tech Report OSU-CISRC-4/06-TR47, April 2006.
• Shape segmentation and matching with flow discretization T. K. Dey, J. Giesen and S. Goswami. Proc. Workshop Algorithms Data Strucutres (WADS 03), LNCS 2748, F. Dehne, J.-R. Sack, M. Smid Eds., 25--36 .

• A simple algorithm for homeomorphic surface reconstruction
  N. Amenta, S. Choi, T. K. Dey and N. Leekha. Intl. Journal on Computational Geometry & Applications, vol. 12, (2002), 125--141
• Critical points of the distance to an epsilon-sampling on a surface and flow-complex- based surface reconstruction.
  T. K. Dey, J. Giesen, E. A. Ramos and B. Sadri. Proc. 21st Annu. Sympos. Comput.  Geom., (2005), 218--227.
• Manifold Reconstruction from Point Samples
  Siu-Wing Cheng, T. K. Dey and E. A. Ramos. Proc. ACM-SIAM Sympos. Discrete Algorithms, 2005, 1018--1027.
  
• Sampling and meshing a surface with guaranteed topology and geometry
  S.-W. Cheng, T. K. Dey, E. Ramos and T. Ray.Proc. 20th Sympos. Comput. Geom. (2004), 280--289
• Dynamic skin triangulation
  H-L. Cheng, T. K. Dey, H. Edelsbrunner and J. Sullivan. Discrete Comput. Geom., vol. 25, (2001), 525--568
  
• T. K. Dey, H. Edelsbrunner, S. Guha and D. Nekhayev. Topology preserving edge contraction. . Publications de l' Institut Mathematique (Beograd), Vol. 60 (80), 1999. Aslo, Technical Report RGI-Tech-98-018, Raindrop geomagic Inc., Research Triangle Park, North Carolina, 1998.
• One of the authors of Emerging Challenges in Computational Topology . (A NSF report), 1999. 
• T. K. Dey and S. Guha. Computing homology groups of simplicial complexes in $R^3$ . Journal of ACM , vol. 45, No. 2, (1998), 266-287. Preliminary version in 28th ACM STOC , 1996, 398-407. 
• T. K. Dey and S. Guha. Transforming curves on surfaces . Journal of Computer and System Sciences, vol. 58, 1999, 297--325. Preliminary version in IEEE FOCS , 1995, 266-274. 
• T. K. Dey, H. Edelsbrunner and S. Guha. Computational Topology . Invited paper in Advances in Discrere and Computational Geometry, eds. B. Chazelle, J. E. Goodman and R. Pollack. Contemporary Mathematics, AMS, Providence, 1998. 
• T. K. Dey. Optimal algorithms to detect null-homologous cycles on 2-manifolds. Intl. Journal of Computational Geometry & Applications, Vol. 7, No. 3, (1997), 167--174. Preliminary version in 5th CCCG , 1993, 273-278. 
• T. K. Dey and H. Schipper. A new technique to compute polygonal schema for 2-manifolds with application to null-homotopy detection. Discrete & Computational Geometry, Vol. 14, 93--110 (1995). Preliminary version in 10th SoCG, 1994, 277-284.