NDLI: Graph induced complex on point data

Please wait, while we are loading the content...

A simple aggregative algorithm for counting triangulations of planar point sets and related problems

Efficiently hex-meshing things with topology

On a forgotten conjecture from a famous paper of Erdös

Graph induced complex on point data

Kinetic data structures for all nearest neighbors and closest pair in the plane

Recent progress on the combinatorial diameter of polyhedra and simplicial complexes

Complexity analysis of random geometric structures made simpler

On the 2-sum embedding conjecture

Range counting coresets for uncertain data

Counting and sampling minimum cuts in genus g graphs

Putting the turing into manufacturing: recent developments in algorithmic automation

A new approach to output-sensitive voronoi diagrams and delaunay triangulations

Ramsey-type results for semi-algebraic relations

Polyominoes on twisted cylinders

On soft predicates in subdivision motion planning

Zigzag zoology: rips zigzags for homology inference

Measuring similarity between curves on 2-manifolds via homotopy area

A sub-quadratic algorithm for bipartite matching of planar points with bounded integer coordinates

Localized delaunay refinement for piecewise-smooth complexes

On planar point sets with the pentagon property

Homological reconstruction and simplification in $R^{3}$

Kinetic 2-centers in the black-box model

Union of random minkowski sums and network vulnerability analysis

Diverse near neighbor problem

Small-size relative (p,ε)-approximations for well-behaved range spaces

Topological graphs: empty triangles and disjoint matchings

A fast algorithm for well-spaced points and approximate delaunay graphs

Sharp bounds on Davenport-Schinzel sequences of every order

Interactive visualization of 3D configuration spaces

A near-optimal algorithm for shortest paths among curved obstacles in the plane

Geometry in the space of persistence modules

Lower bounds for k-distance approximation

A faster algorithm for computing motorcycle graphs

A parallel algorithm for computing the flow complex

Equal coefficients and tolerance in coloured tverberg partitions

Parameterized complexity of discrete morse theory

Competitive query strategies for minimising the ply of the potential locations of moving points

The maximum number of faces of the minkowski sum of three convex polytopes

Compressive sensing using locality-preserving matrices

A constant-factor approximation for multi-covering with disks

Bichromatic compatible matchings

Fast segment insertion and incremental construction of constrained delaunay triangulations

Capture bounds for visibility-based pursuit evasion

Parametric search visualization

Computing shortest paths among curved obstacles in the plane

Computing closed essential surfaces in knot complements

Systems of distant representatives in euclidean space

The graphs of planar soap bubbles

Hyperbolic delaunay complexes and voronoi diagrams made practical

Improved bounds for incidences between points and circles

Triangulating unknown environments using robot swarms

The complexity of separating points in the plane

A new approach to crushing 3-manifold triangulations

Robust geometric spanners

Point guards and point clouds: solving general art gallery problems

Graph induced complex on point data

Content Provider	ACM Digital Library
Author	Dey, Tamal Krishna Fan, Fengtao Wang, Yusu
Abstract	The efficiency of extracting topological information from point data depends largely on the complex that is built on top of the data points. From a computational viewpoint, the most favored complexes for this purpose have so far been Vietoris-Rips and witness complexes. While the ietoris-Rips complex is simple to compute and is a good vehicle for extracting topology of sampled spaces, its size is huge--particularly in high dimensions. The witness complex on the other hand enjoys a smaller size because of a subsampling, but fails to capture the topology in high dimensions unless imposed with extra structures. We investigate a complex called the graph induced complex that, to some extent, enjoys the advantages of both. It works on a subsample but still retains the power of capturing the topology as the Vietoris-Rips complex. It only needs a graph connecting the original sample points from which it builds a complex on the subsample thus taming the size considerably. We show that, using the graph induced complex one can (i) infer the one-dimensional homology of a manifold from a very lean subsample, (ii) reconstruct a surface in three dimension from a sparse subsample without computing Delaunay triangulations, (iii) infer the persistent homology groups of compact sets from a sufficiently dense sample. We provide experimental evidences in support of our theory.
Starting Page	107
Ending Page	116
Page Count	10
File Format	PDF
ISBN	9781450320313
DOI	10.1145/2462356.2462387
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2013-06-17
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Graph induced complex Surface reconstruction Homology Topological data analysis
Content Type	Text
Resource Type	Article

Central Library (ISO-9001:2015 Certified)
Indian Institute of Technology Kharagpur
Kharagpur, West Bengal, India | PIN - 721302

See location in the Map
03222 282435
Mail: support@ndl.gov.in

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in