TY - GEN

T1 - On the general chain pair simplification problem

AU - Fan, Chenglin

AU - Filtser, Omrit

AU - Katz, Matthew J.

AU - Zhu, Binhai

N1 - Publisher Copyright:
© Yuta Fujishige, Yuki Tsujimaru, Shunsuke Inenaga, Hideo Bannai, and Masayuki Takeda.

PY - 2016/8/1

Y1 - 2016/8/1

N2 - The Chain Pair Simplification problem (CPS) was posed by Bereg et al. who were motivated by the problem of efficiently computing and visualizing the structural resemblance between a pair of protein backbones. In this problem, given two polygonal chains of lengths n and m, the goal is to simplify both of them simultaneously, so that the lengths of the resulting simplifications as well as the discrete Fréchet distance between them are bounded. When the vertices of the simplifications are arbitrary (i.e., not necessarily from the original chains), the problem is called General CPS (GCPS). In this paper we consider for the first time the complexity of GCPS under both the discrete Fréchet distance (GCPS-3F) and the Hausdorff distance (GCPS-2H). (In the former version, the quality of the two simplifications is measured by the discrete Fréchet distance, and in the latter version it is measured by the Hausdorff distance.) We prove that GCPS-3F is polynomially solvable, by presenting an eO((n+m)6 min{n,m}) time algorithm for the corresponding minimization problem. We also present an O((n + m)4) 2-approximation algorithm for the problem. On the other hand, we show that GCPS-2H is NP-complete, and present an approximation algorithm for the problem.

AB - The Chain Pair Simplification problem (CPS) was posed by Bereg et al. who were motivated by the problem of efficiently computing and visualizing the structural resemblance between a pair of protein backbones. In this problem, given two polygonal chains of lengths n and m, the goal is to simplify both of them simultaneously, so that the lengths of the resulting simplifications as well as the discrete Fréchet distance between them are bounded. When the vertices of the simplifications are arbitrary (i.e., not necessarily from the original chains), the problem is called General CPS (GCPS). In this paper we consider for the first time the complexity of GCPS under both the discrete Fréchet distance (GCPS-3F) and the Hausdorff distance (GCPS-2H). (In the former version, the quality of the two simplifications is measured by the discrete Fréchet distance, and in the latter version it is measured by the Hausdorff distance.) We prove that GCPS-3F is polynomially solvable, by presenting an eO((n+m)6 min{n,m}) time algorithm for the corresponding minimization problem. We also present an O((n + m)4) 2-approximation algorithm for the problem. On the other hand, we show that GCPS-2H is NP-complete, and present an approximation algorithm for the problem.

KW - Chain simplification

KW - Discrete Fréchet distance

KW - Dynamic programming

KW - Geometric arrangements

KW - Protein structural resemblance

UR - http://www.scopus.com/inward/record.url?scp=85012910659&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.MFCS.2016.37

DO - 10.4230/LIPIcs.MFCS.2016.37

M3 - Conference contribution

AN - SCOPUS:85012910659

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016

A2 - Muscholl, Anca

A2 - Faliszewski, Piotr

A2 - Niedermeier, Rolf

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016

Y2 - 22 August 2016 through 26 August 2016

ER -