Strong Collapse for Persistence

Divyansh Pareek; Jean-Daniel Boissonnat; Siddharth Pritam

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Strong Collapse for Persistence

Jean-Daniel Boissonnat, Siddharth Pritam, Divyansh Pareek

Computational Geometry · Submitted 28 Sep 2018

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim As a result and as demonstrated by numerous experiments on publicly available data sets, our approach is extremely fast and memory efficient in practice.

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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 6,856 input tokens.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.45 · human participants 0.02 · controlled comparison 0.07 · randomized assignment 0.01 · states quantitative result 0.08 · compares with prior results 0.63 · mentions code or data availability 0.06.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We introduce a fast and memory efficient approach to compute the persistent homology (PH) of a sequence of simplicial complexes. The basic idea is to simplify the complexes of the input sequence by using strong collapses, as introduced by J. Barmak and E. Miniam [DCG (2012)], and to compute the PH of an induced sequence of reduced simplicial complexes that has the same PH as the initial one. Our approach has several salient features that distinguishes it from previous work. It is not limited to filtrations (i.e. sequences of nested simplicial subcomplexes) but works for other types of sequences like towers and zigzags. To strong collapse a simplicial complex, we only need to store the maximal simplices of the complex, not the full set of all its simplices, which saves a lot of space and time. Moreover, the complexes in the sequence can be strong collapsed independently and in parallel. Finally, we can compromize between precision and time by choosing the number of simplicial complexes of the sequence we strong collapse. As a result and as demonstrated by numerous experiments on publicly available data sets, our approach is extremely fast and memory efficient in practice.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We introduce a fast and memory efficient approach to compute the persistent homology (PH) of a sequence of simplicial complexes.	contribution 1.00	0.92	0.22	asserted 1.00
s1	The basic idea is to simplify the complexes of the input sequence by using strong collapses, as introduced by J. Barmak and E.	method 0.96	0.25	0.06	asserted 0.99
s2	Miniam [DCG (2012)], and to compute the PH of an induced sequence of reduced simplicial complexes that has the same PH as the initial one.	method 0.91	0.42	0.11	asserted 0.93
s3	Our approach has several salient features that distinguishes it from previous work.	contribution 0.93	0.37	0.03	asserted 0.94
s4	It is not limited to filtrations (i.e. sequences of nested simplicial subcomplexes) but works for other types of sequences like towers and zigzags.	contribution 0.97	0.66	0.05	asserted 1.00
s5	To strong collapse a simplicial complex, we only need to store the maximal simplices of the complex, not the full set of all its simplices, which saves a lot of space and time.	method 0.91	0.68	0.10	asserted 1.00
s6	Moreover, the complexes in the sequence can be strong collapsed independently and in parallel.	method 0.53	0.71	0.05	asserted 0.96
s7	Finally, we can compromize between precision and time by choosing the number of simplicial complexes of the sequence we strong collapse.	method 0.61	0.80	0.07	asserted 0.71
s8	As a result and as demonstrated by numerous experiments on publicly available data sets, our approach is extremely fast and memory efficient in practice.	result 0.98	0.95	0.75	asserted 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from observation or experiment 0.54.

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arXiv listing abstract v1

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full text
figures and tables
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S sections
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C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

We introduce a fast and memory efficient approach to compute the persistent homology (PH) of a sequence of simplicial complexes. The basic idea is to simplify the complexes of the input sequence by using strong collapses, as introduced by J. Barmak and E. Miniam [DCG (2012)], and to compute the PH of an induced sequence of reduced simplicial complexes that has the same PH as the initial one. Our approach has several salient features that distinguishes it from previous work. It is not limited to filtrations (i.e. sequences of nested simplicial subcomplexes) but works for other types of sequences like towers and zigzags. To strong collapse a simplicial complex, we only need to store the maximal simplices of the complex, not the full set of all its simplices, which saves a lot of space and time. Moreover, the complexes in the sequence can be strong collapsed independently and in parallel. Finally, we can compromize between precision and time by choosing the number of simplicial complexes of the sequence we strong collapse. As a result and as demonstrated by numerous experiments on publicly available data sets, our approach is extremely fast and memory efficient in practice.

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How the literature uses it

3 arXiv papers cite this in 6 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 5 sentences without a confident label

Compares with it 1 paper

Notably, [ref] observes that a scheme to simplify complexes is trivially parallelizable for reasons similar to the trivial parallelization of induced maps, and [ref] describes a parallelization scheme that has similarities to our quiver scheme, but operates on chain complexes and not induced maps on homology.

Persistent and Zigzag Homology: A Matrix Factorization Viewpoint · Contributions and Related Work · 0.95

What it cites

Uses the method or tool of 1 paper

We then convert the core tower into an equivalent filtration using the Sophia software [ref] , which implements the algorithm described by Kerber and Schreiber in [ref] .

Barcodes of Towers and a Streaming Algorithm for Persistent Homology · Computational experiments · 1.00

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