Computational Topology and Data Analysis Papers

• [deSilva-Carlsson04] Topological estimation using witness complexes. Vin de Silva and Gunnar Carlsson. Eurographics Sympos. Point-Based Graphics (2004).
  
• [DeyFanWang13]  Graph induced complex on point data. T. K. Dey, F. Fan, and Y. Wang. to appear in 29th Annual Sympos. Comput. Geom. (SoCG) 2013.
• [EdelsbrunnerLetscherZomorodian02] Topological persistence and simplification. H. Edelsbrunner, D. Letscher, and A. Zomorodian. Discsre Comput. Geom., 28, 511-533, (2002).
• [ZomorodianCarlsson04] Computing persistent homology. A. Zomorodian and G. Carlsson. Discrete & Comput. Geom., 33, 249--274 (2005).
• [Cohen-SteinerEdelsbrunnerHarer07] Stability of persistence diagrams. D. Cohen-Steiner, H. Edelsbrunner, and J. Harer. Discrete & Comput. Geom., 37, 103--120 (2007).
  
• [CarlssonSilvaMorozov09] Zigzag persistent homology and real-valued functions. G. Carlsson, V. de Silva, and D. Morozov. Proc. Annu. Sympos. Comput. Geom. (2009), 247--256.
• [DeyFanWang13SM] Computing topological persistence for simplicial maps.  T. K. Dey, F. Fan, and Y. Wang. Manuscript, October, 2012, arXiv:1208.5018v2
• [AmentaBernEppstein98] The crust and the b-skeleton: combinatorial curve reconstruction. N. Amenta, M. Bern, and D. Eppstein. Graphical Models and Image Proc., 60, 125-135, 1998.
• [AmentaBern99] Surface reconstruction by Voronoi filtering. Proc. 14th Annu. Sympos. Comput. Geom. (1998), 39-48.
  
• [AmentaChoiDeyLeekha01]  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.
• [NiyogiSmaleWeinberger06] Finding the homology of submanifolds with high confidence from random samples. P. Niyogi, S. Smale, and S. Weinberger. Discrete Comput. Geom., 39, 419--441 (2008).
• [ChazalCohen-SteinerLieutier09] A sampling theory for compacts in Euclidean space . F. Chazal, D. Cohen-Steiner, and A. Lieutier. Discrete Comput. Geom. 41, 461--479 (2009).
• [ChengDeyRamos05] Manifold reconstruction from point samples. Proc. ACM-SIAM Sympos. Discrete Algorithms (SODA), 1018-1027 (2005).
  
• [ChazalOudot08] Towards persistence-based reconstruction in Euclidean spaces. F. Chazal and S. Oudot. Proc. Annu. Sympos. Comput. Geom. (2008), 232--241.
• [CCGGO09] Proximity of persistence modules and their diagrams. F. Chazal, D. Cohen-Steiner, M. Glisse, L. Guibas, and S. Oudot. Proc. 25th Annu. Sympos. Comput. Geom. (2009), 237-246.
• [Sheehy12] Linear-size approximations to theVietoris-Rips filtration. D. Sheehy. Proc. 28th Annu. Sympos. Comput. Geom. (2012), 239-248.
• [EricksonWhittlesey05] Greedy optimal homotopy and homology generators. J. Erickson and K. Whittlesey. Proc. Sixteenth ACM-SIAM Sympos. Discrete Algorithms (2005), 1038--1046.
• [DeySunWang09] Approximating cycles in a shortest basis of the first homology group from point data. T. K. Dey, J. Sun, and Y. Wang. Inverse Problems, 27 (2011).
• [DeyHiraniKrishnamoorthy10] Optimal homologous cycles, total unimodularity, and linear programming. T. K. Dey, A. Hirani, B. Krishnamoorthy. SIAM J, Comput., 40, 1026-1044 (2011).
• [C-MEHNP04]  Loops in Reeb graphs of 2-manifolds. K. C-McLaughlin, H. Edelsbrunner, J. Harer, V. Natarajan, and V. Pascucci. Discrete & Comput. Geom., 32, 231-244 (2004).
• [DeyWang11] Reeb graphs: approximation and persistence. T. K. Dey and Y. Wang. Discrete & Comput. Geom., 49, 46--73 (2013)
• [BelkinNiyogi03] Laplacian eigenmaps for dimensionality reduction and data representation. M. Belkin and P. Niyogi. Neural Computation, 15, 1373--1396, 2003.
• [BelkinSunWang09] Constructing Laplace operator from point clouds in R^d. M. Belkin, J. Sun, and Y. Wang. ACM-SIAM Sympos. Discrete Algorithms (SODA)(2009), 1031-1040.
  
• [DeyWang10] Convergence, stability, and discrete approximation of Laplace spectra. T. K. Dey, P. Ranjan, and Y. Wang. Proc. ACM-SIAM Sympos. Discrete Algorithms (SODA) (2010), 650-663.
  

•  Emerging Challenges in Computational Topology . (A NSF report), 1999. 
•  Computational Topology . T. K. Dey, H. Edelsbrunner and S. Guha. Invited paper in Advances in Discrere and Computational Geometry, eds. B. Chazelle, J. E. Goodman and R. Pollack. Contemporary Mathematics, AMS, Providence, 1998.