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 - 2015/1/1

Y1 - 2015/1/1

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 - http://www.scopus.com/inward/record.url?scp=84951853794&partnerID=8YFLogxK

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

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

M3 - Conference contribution

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 -