IEICE TRANSACTIONS on Information
Bicolored Path Embedding Problems Inspired by Protein Folding Models
Summary :
In this paper, we introduce a path embedding problem inspired by the well-known hydrophobic-polar (HP) model of protein folding. A graph is said bicolored if each vertex is assigned a label in the set {red, blue}. For a given bicolored path P and a given bicolored graph G, our problem asks whether we can embed P into G in such a way as to match the colors of the vertices. In our model, G represents a protein's “blueprint,” and P is an amino acid sequence that has to be folded to form (part of) G. We first show that the bicolored path embedding problem is NP-complete even if G is a rectangular grid (a typical scenario in protein folding models) and P and G have the same number of vertices. By contrast, we prove that the problem becomes tractable if the height of the rectangular grid G is constant, even if the length of P is independent of G. Our proof is constructive: we give a polynomial-time algorithm that computes an embedding (or reports that no embedding exists), which implies that the problem is in XP when parameterized according to the height of G. Additionally, we show that the problem of embedding P into a rectangular grid G in such a way as to maximize the number of red-red contacts is NP-hard. (This problem is directly inspired by the HP model of protein folding; it was previously known to be NP-hard if G is not given, and P can be embedded in any way on a grid.) Finally, we show that, given a bicolored graph G, the problem of constructing a path P that embeds in G maximizing red-red contacts is Poly-APX-hard.
- Publication
- IEICE TRANSACTIONS on Information Vol.E105-D No.3 pp.623-633
- Publication Date
- 2022/03/01
- Publicized
- 2021/12/07
- Online ISSN
- 1745-1361
- DOI
- 10.1587/transinf.2021EDP7206
- Type of Manuscript
- PAPER
- Category
- Fundamentals of Information Systems
Authors
Tianfeng FENG
Japan Advanced Institute of Science and Technology (JAIST)
Ryuhei UEHARA
Japan Advanced Institute of Science and Technology (JAIST)
Giovanni VIGLIETTA
Japan Advanced Institute of Science and Technology (JAIST)
Keyword
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Tianfeng FENG, Ryuhei UEHARA, Giovanni VIGLIETTA, "Bicolored Path Embedding Problems Inspired by Protein Folding Models" in IEICE TRANSACTIONS on Information,
vol. E105-D, no. 3, pp. 623-633, March 2022, doi: 10.1587/transinf.2021EDP7206.
Abstract: In this paper, we introduce a path embedding problem inspired by the well-known hydrophobic-polar (HP) model of protein folding. A graph is said bicolored if each vertex is assigned a label in the set {red, blue}. For a given bicolored path P and a given bicolored graph G, our problem asks whether we can embed P into G in such a way as to match the colors of the vertices. In our model, G represents a protein's “blueprint,” and P is an amino acid sequence that has to be folded to form (part of) G. We first show that the bicolored path embedding problem is NP-complete even if G is a rectangular grid (a typical scenario in protein folding models) and P and G have the same number of vertices. By contrast, we prove that the problem becomes tractable if the height of the rectangular grid G is constant, even if the length of P is independent of G. Our proof is constructive: we give a polynomial-time algorithm that computes an embedding (or reports that no embedding exists), which implies that the problem is in XP when parameterized according to the height of G. Additionally, we show that the problem of embedding P into a rectangular grid G in such a way as to maximize the number of red-red contacts is NP-hard. (This problem is directly inspired by the HP model of protein folding; it was previously known to be NP-hard if G is not given, and P can be embedded in any way on a grid.) Finally, we show that, given a bicolored graph G, the problem of constructing a path P that embeds in G maximizing red-red contacts is Poly-APX-hard.
URL: https://global.ieice.org/en_transactions/information/10.1587/transinf.2021EDP7206/_p
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@ARTICLE{e105-d_3_623,
author={Tianfeng FENG, Ryuhei UEHARA, Giovanni VIGLIETTA, },
journal={IEICE TRANSACTIONS on Information},
title={Bicolored Path Embedding Problems Inspired by Protein Folding Models},
year={2022},
volume={E105-D},
number={3},
pages={623-633},
abstract={In this paper, we introduce a path embedding problem inspired by the well-known hydrophobic-polar (HP) model of protein folding. A graph is said bicolored if each vertex is assigned a label in the set {red, blue}. For a given bicolored path P and a given bicolored graph G, our problem asks whether we can embed P into G in such a way as to match the colors of the vertices. In our model, G represents a protein's “blueprint,” and P is an amino acid sequence that has to be folded to form (part of) G. We first show that the bicolored path embedding problem is NP-complete even if G is a rectangular grid (a typical scenario in protein folding models) and P and G have the same number of vertices. By contrast, we prove that the problem becomes tractable if the height of the rectangular grid G is constant, even if the length of P is independent of G. Our proof is constructive: we give a polynomial-time algorithm that computes an embedding (or reports that no embedding exists), which implies that the problem is in XP when parameterized according to the height of G. Additionally, we show that the problem of embedding P into a rectangular grid G in such a way as to maximize the number of red-red contacts is NP-hard. (This problem is directly inspired by the HP model of protein folding; it was previously known to be NP-hard if G is not given, and P can be embedded in any way on a grid.) Finally, we show that, given a bicolored graph G, the problem of constructing a path P that embeds in G maximizing red-red contacts is Poly-APX-hard.},
keywords={},
doi={10.1587/transinf.2021EDP7206},
ISSN={1745-1361},
month={March},}
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TY - JOUR
TI - Bicolored Path Embedding Problems Inspired by Protein Folding Models
T2 - IEICE TRANSACTIONS on Information
SP - 623
EP - 633
AU - Tianfeng FENG
AU - Ryuhei UEHARA
AU - Giovanni VIGLIETTA
PY - 2022
DO - 10.1587/transinf.2021EDP7206
JO - IEICE TRANSACTIONS on Information
SN - 1745-1361
VL - E105-D
IS - 3
JA - IEICE TRANSACTIONS on Information
Y1 - March 2022
AB - In this paper, we introduce a path embedding problem inspired by the well-known hydrophobic-polar (HP) model of protein folding. A graph is said bicolored if each vertex is assigned a label in the set {red, blue}. For a given bicolored path P and a given bicolored graph G, our problem asks whether we can embed P into G in such a way as to match the colors of the vertices. In our model, G represents a protein's “blueprint,” and P is an amino acid sequence that has to be folded to form (part of) G. We first show that the bicolored path embedding problem is NP-complete even if G is a rectangular grid (a typical scenario in protein folding models) and P and G have the same number of vertices. By contrast, we prove that the problem becomes tractable if the height of the rectangular grid G is constant, even if the length of P is independent of G. Our proof is constructive: we give a polynomial-time algorithm that computes an embedding (or reports that no embedding exists), which implies that the problem is in XP when parameterized according to the height of G. Additionally, we show that the problem of embedding P into a rectangular grid G in such a way as to maximize the number of red-red contacts is NP-hard. (This problem is directly inspired by the HP model of protein folding; it was previously known to be NP-hard if G is not given, and P can be embedded in any way on a grid.) Finally, we show that, given a bicolored graph G, the problem of constructing a path P that embeds in G maximizing red-red contacts is Poly-APX-hard.
ER -
English
