Computational topology papers

Computational Topology

Computing optimal persistent cycles for levelset zigzag on manifold-like complexes T. K. Dey, T. Hou, arXiv: https://arxiv.org/abs/2105.00518 May 2021.
Computing zigzag persistence on graphs in near-linear time T. K. Dey, T. Hou, March 2021, Proc. Internat. Sympos. Comput. Geom. (2021) (SoCG 2021).
Persistence of the Conley Index in Combinatorial Dynamical Systems T. K. Dey, M. Mrozek, and R. Slechta, February 2020, Proc. Internat. Sympos. Comput. Geom. (2020) (SoCG 2020).
An efficient algorithm for 1-dimensional (persistent) path homology T. K. Dey, T. Li, and Y. Wang, January 2020, arxiv:https://arxiv.org/abs/2001.09549, Proc. Internat. Sympos. Comput. Geom. (2020) (SoCG 2020).
Generalized Persistence Algorithm for Decomposing Multi-parameter Persistence Modules T. K. Dey and Cheng Xin ., May 2019, arxiv: https://arxiv.org/abs/1904.03766
Computing Minimal Persistent Cycles: Polynomial and Hard Cases T. K. Dey, T. Hou, and S. Mandal. Proceedings ACM-SIAM Sympos. Discrete Algorithms (SODA 20),July 2019, arxiv: https://arxiv.org/abs/1907.04889
Persistent homology of Morse decompositions in combinatorial dynamics T. K. Dey, M. Juda, T. Kapela, J. Kubica, M. Lipinski, M. Mrozek. https://arxiv.org/abs/1801.06590. 2018. SIAM J. on Applied Dynamical System, Vol. 18, Issue 1, 510--530, 2019.
Computing Bottleneck Distance for 2-D Interval Decomposable Modules T. K. Dey, C. Xin. Proc. 34th Internat. Sympos. Comput. Geoem., 32:1--32:15 (SoCG 2018).
Graph Reconstruction by Discrete Morse Theory T. K. Dey, J. Wang and Y. Wang. Proc. Internat. Sympos. Comput. Geom., 31:1--31:15 (SoCG 2018).
Efficient Algorithms for Computing a Minimal Homology Basis T. K. Dey, T. Li, and Y. Wang. Proc. LATIN 2018: Theoretical Informatics, LNCS, Vol. 10807, 376--398 (LATIN 2018).
Topological analysis of nerves, Reeb spaces, mappers, and multiscale mappers T. K. Dey, F. Memoli, and Y. Wang. Proc. Internat. Sympos. Comput. Geom. (2017) (SoCG 2017).
SimBa: An efficient tool for approximating Rips-filtration persistence via Simplicial Batch-collapse T. K. Dey, D. Shi, and Y. Wang. European Symposium on Algorithms (ESA 2016).
Multiscale Mapper: Topological summarization via codomain covers T. K. Dey, F. Memoli, and Y. Wang. ACM-SIAM Sympos. Discrete Algorithms (SODA 2016)
Comparing graphs via persistence distortion T. K. Dey, D. Shi and Y. Wang. 31st Annu. Sympos. Comput. Geom. (SoCG 15).
Dimension detection with local homology. T. K. Dey, F. Fan, and Y. Wang. 2014, arXiv: 1405.3534.
Computing topological persistence for simplicial maps. T. K. Dey, F. Fan, Y. Wang, 30th Annual Sympos. Comput. Geom. (SoCG 2014), to appear.
Graph induced complex on point data. T. K. Dey, F. Fan, and Y. Wang. 29th Annual Sympos. Comput. Geom. (SoCG 2013), 107--116.
Edge contractions and simplicial homology. T. K. Dey, A. N. Hirani, B. Krishnamoorthy, and G. Smith. April, 2013. arXiv:1304.0664
Annotating simplices with a homology basis and its applications. O. Busaryev, S. Cabello, C. Chen, T. K. Dey, and Y. Wang. 13th Scandinavian Sympos. Workshops Algorithm Theory (SWAT 2012). Lecture Notes in Computer Science Volume 7357, 2012, pp 189-200.
Topological Persistence for circle valued maps. D. Burghelea and T. K. Dey. Discrete & Comput. Geometry, Vol. 50, No. 1 (2013), 69--98. An earlier version arXiv:1104.5646. April, 2011.
Reeb graphs: approximation and persistence. T. K. Dey and Y. Wang. Proc. 27th Annu. Sympos. Comput. Geom. (SOCG 2011), 226--235. Journal version in Discrete & Comput. Geom., Vol. 49 (2013), 46--73.
Approximating loops in a shortest homology basis from point data. T. K. Dey, J. Sun, and Y. Wang. 26th. Annu. Sympos. Comput. Geom. (SoCG 2010), 166-175.
Optimal homologous cycles, total unimodularity, and linear programming. T. K. Dey, A. Hirani, and B. Krishnamoorthy. 42nd ACM Sympos. Theory Computing (STOC 2010), 221--230.
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.
Cut locus and topology from surface point data. T. K. Dey and K. Li. 25th Ann. Sympos. Comput. Geom. (SoCG 2009), 125--134.
Computing geometry-aware handle and tunnel loops in 3D models. T. K. Dey, K. Li, J. Sun, and D. Cohen-Steiner. SIGGRAPH 2008, 45:1--45:9.
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 (SODA07), 1096--1105.
Stability of critical points with interval persistence T. K. Dey and R. Wenger. Discrete & Computational Geometry, Vol. 38 (2007) 479--512 . 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., (SoCG 2005), 218--227.
Manifold Reconstruction from Point Samples Siu-Wing Cheng, T. K. Dey and E. A. Ramos. Proc. ACM-SIAM Sympos. Discrete Algorithms, (SODA 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
Topology preserving edge contraction. .T. K. Dey, H. Edelsbrunner, S. Guha and D. Nekhayev. 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.
Computing homology groups of simplicial complexes in $R^3$ .T. K. Dey and S. Guha. Journal of ACM , vol. 45, No. 2, (1998), 266-287. Preliminary version in 28th ACM STOC , 1996, 398-407.
Transforming curves on surfaces .T. K. Dey and S. Guha. Journal of Computer and System Sciences, vol. 58, 1999, 297--325. Preliminary version in IEEE FOCS , 1995, 266-274.
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.
Optimal algorithms to detect null-homologous cycles on 2-manifolds. T. K. Dey.Intl. Journal of Computational Geometry & Applications, Vol. 7, No. 3, (1997), 167--174. Preliminary version in 5th CCCG , 1993, 273-278.
A new technique to compute polygonal schema for 2-manifolds with application to null-homotopy detection.T. K. Dey and H. Schipper. Discrete & Computational Geometry, Vol. 14, 93--110 (1995). Preliminary version in 10th SoCG, 1994, 277-284.

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