On the chain pair simplification problem

Chenglin Fan; Omrit Filtser; Matthew J. Katz; Tim Wylie; Binhai Zhu

doi:10.1007/978-3-319-21840-3_29

On the chain pair simplification problem

Chenglin Fan, Omrit Filtser, Matthew J. Katz, Tim Wylie, Binhai Zhu

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

The problem of efficiently computing and visualizing the structural resemblance between a pair of protein backbones in 3D has led Bereg et al. [4] to pose the Chain Pair Simplification problem (CPS). In this problem, given two polygonal chains A and B of lengths m and n, respectively, one needs to simplify them simultaneously, such that each of the resulting simplified chains, Aʹ and Bʹ, is of length at most k and the discrete Fréchet distance between Aʹ and Bʹ is at most δ, where k and δ are given parameters. In this paper we study the complexity of CPS under the discrete Fréchet distance (CPS-3F), i.e., where the quality of the simplifications is also measured by the discrete Fréchet distance. Since CPS-3F was posed in 2008, its complexity has remained open. In this paper, we prove that CPS-3F is actually polynomially solvable, by presenting an O(m²n² min{m, n}) time algorithm for the corresponding minimization problem. On the other hand, we prove that if the vertices of the chains have integral weights then the problem is weakly NP-complete.

Original language	English
Title of host publication	Algorithms and Data Structures - 14th International Symposium, WADS 2015, Proceedings
Editors	Frank Dehne, Jorg-Rudiger Sack, Ulrike Stege
Publisher	Springer Verlag
Pages	351-362
Number of pages	12
ISBN (Print)	9783319218397
DOIs	https://doi.org/10.1007/978-3-319-21840-3_29
State	Published - 2015
Externally published	Yes
Event	14th International Symposium on Algorithms and Data Structures, WADS 2015 - Victoria, Canada Duration: 5 Aug 2015 → 7 Aug 2015

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	9214
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	14th International Symposium on Algorithms and Data Structures, WADS 2015
Country/Territory	Canada
City	Victoria
Period	5/08/15 → 7/08/15

Bibliographical note

Publisher Copyright:
© Springer International Publishing Switzerland 2015.

Access to Document

10.1007/978-3-319-21840-3_29

Cite this

Fan, C., Filtser, O., Katz, M. J., Wylie, T., & Zhu, B. (2015). On the chain pair simplification problem. In F. Dehne, J.-R. Sack, & U. Stege (Eds.), Algorithms and Data Structures - 14th International Symposium, WADS 2015, Proceedings (pp. 351-362). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9214). Springer Verlag. https://doi.org/10.1007/978-3-319-21840-3_29

Fan, Chenglin ; Filtser, Omrit ; Katz, Matthew J. et al. / On the chain pair simplification problem. Algorithms and Data Structures - 14th International Symposium, WADS 2015, Proceedings. editor / Frank Dehne ; Jorg-Rudiger Sack ; Ulrike Stege. Springer Verlag, 2015. pp. 351-362 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

@inproceedings{d6da0cebed344733b52c0b273c6f6984,

title = "On the chain pair simplification problem",

abstract = "The problem of efficiently computing and visualizing the structural resemblance between a pair of protein backbones in 3D has led Bereg et al. [4] to pose the Chain Pair Simplification problem (CPS). In this problem, given two polygonal chains A and B of lengths m and n, respectively, one needs to simplify them simultaneously, such that each of the resulting simplified chains, Aʹ and Bʹ, is of length at most k and the discrete Fr{\'e}chet distance between Aʹ and Bʹ is at most δ, where k and δ are given parameters. In this paper we study the complexity of CPS under the discrete Fr{\'e}chet distance (CPS-3F), i.e., where the quality of the simplifications is also measured by the discrete Fr{\'e}chet distance. Since CPS-3F was posed in 2008, its complexity has remained open. In this paper, we prove that CPS-3F is actually polynomially solvable, by presenting an O(m2n2 min\{m, n\}) time algorithm for the corresponding minimization problem. On the other hand, we prove that if the vertices of the chains have integral weights then the problem is weakly NP-complete.",

author = "Chenglin Fan and Omrit Filtser and Katz, \{Matthew J.\} and Tim Wylie and Binhai Zhu",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2015.; 14th International Symposium on Algorithms and Data Structures, WADS 2015 ; Conference date: 05-08-2015 Through 07-08-2015",

year = "2015",

doi = "10.1007/978-3-319-21840-3\_29",

language = "אנגלית",

isbn = "9783319218397",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "351--362",

editor = "Frank Dehne and Jorg-Rudiger Sack and Ulrike Stege",

booktitle = "Algorithms and Data Structures - 14th International Symposium, WADS 2015, Proceedings",

address = "גרמניה",

}

Fan, C, Filtser, O, Katz, MJ, Wylie, T & Zhu, B 2015, On the chain pair simplification problem. in F Dehne, J-R Sack & U Stege (eds), Algorithms and Data Structures - 14th International Symposium, WADS 2015, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9214, Springer Verlag, pp. 351-362, 14th International Symposium on Algorithms and Data Structures, WADS 2015, Victoria, Canada, 5/08/15. https://doi.org/10.1007/978-3-319-21840-3_29

On the chain pair simplification problem. / Fan, Chenglin; Filtser, Omrit; Katz, Matthew J. et al.
Algorithms and Data Structures - 14th International Symposium, WADS 2015, Proceedings. ed. / Frank Dehne; Jorg-Rudiger Sack; Ulrike Stege. Springer Verlag, 2015. p. 351-362 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9214).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - On the chain pair simplification problem

AU - Fan, Chenglin

AU - Filtser, Omrit

AU - Katz, Matthew J.

AU - Wylie, Tim

AU - Zhu, Binhai

N1 - Publisher Copyright: © Springer International Publishing Switzerland 2015.

PY - 2015

Y1 - 2015

N2 - The problem of efficiently computing and visualizing the structural resemblance between a pair of protein backbones in 3D has led Bereg et al. [4] to pose the Chain Pair Simplification problem (CPS). In this problem, given two polygonal chains A and B of lengths m and n, respectively, one needs to simplify them simultaneously, such that each of the resulting simplified chains, Aʹ and Bʹ, is of length at most k and the discrete Fréchet distance between Aʹ and Bʹ is at most δ, where k and δ are given parameters. In this paper we study the complexity of CPS under the discrete Fréchet distance (CPS-3F), i.e., where the quality of the simplifications is also measured by the discrete Fréchet distance. Since CPS-3F was posed in 2008, its complexity has remained open. In this paper, we prove that CPS-3F is actually polynomially solvable, by presenting an O(m2n2 min{m, n}) time algorithm for the corresponding minimization problem. On the other hand, we prove that if the vertices of the chains have integral weights then the problem is weakly NP-complete.

AB - The problem of efficiently computing and visualizing the structural resemblance between a pair of protein backbones in 3D has led Bereg et al. [4] to pose the Chain Pair Simplification problem (CPS). In this problem, given two polygonal chains A and B of lengths m and n, respectively, one needs to simplify them simultaneously, such that each of the resulting simplified chains, Aʹ and Bʹ, is of length at most k and the discrete Fréchet distance between Aʹ and Bʹ is at most δ, where k and δ are given parameters. In this paper we study the complexity of CPS under the discrete Fréchet distance (CPS-3F), i.e., where the quality of the simplifications is also measured by the discrete Fréchet distance. Since CPS-3F was posed in 2008, its complexity has remained open. In this paper, we prove that CPS-3F is actually polynomially solvable, by presenting an O(m2n2 min{m, n}) time algorithm for the corresponding minimization problem. On the other hand, we prove that if the vertices of the chains have integral weights then the problem is weakly NP-complete.

UR - https://www.scopus.com/pages/publications/84951853794

U2 - 10.1007/978-3-319-21840-3_29

DO - 10.1007/978-3-319-21840-3_29

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:84951853794

SN - 9783319218397

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 351

EP - 362

BT - Algorithms and Data Structures - 14th International Symposium, WADS 2015, Proceedings

A2 - Dehne, Frank

A2 - Sack, Jorg-Rudiger

A2 - Stege, Ulrike

PB - Springer Verlag

T2 - 14th International Symposium on Algorithms and Data Structures, WADS 2015

Y2 - 5 August 2015 through 7 August 2015

ER -

Fan C, Filtser O, Katz MJ, Wylie T, Zhu B. On the chain pair simplification problem. In Dehne F, Sack JR, Stege U, editors, Algorithms and Data Structures - 14th International Symposium, WADS 2015, Proceedings. Springer Verlag. 2015. p. 351-362. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-319-21840-3_29

On the chain pair simplification problem

Abstract

Publication series

Conference

Bibliographical note

Access to Document

Other files and links

Fingerprint

Cite this