## Abstract

In the MAXIMUM INTERVAL CONSTRAINED COLORING problem, we are given a set of vertices and a set of intervals on a line and a k-dimensional requirement vector for each interval, specifying how many vertices of each of k colors should appear in the interval. The objective is to color the vertices of the line with k colors so as to maximize the total weight of intervals for which the requirement is satisfied. This NP-hard combinatorial problem arises in the interpretation of data on protein structure emanating from experiments based on hydrogen/deuterium exchange and mass spectrometry. For constant k, we give a factor O(|Opt|)-approximation algorithm, where Opt is the smallest cardinality maximum-weight solution. We show further that, even for k=2, the problem remains APX-hard.

Original language | British English |
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Pages (from-to) | 57-72 |

Number of pages | 16 |

Journal | Discrete Optimization |

Volume | 27 |

DOIs | |

State | Published - Feb 2018 |

## Keywords

- Approximation algorithms
- APX-hardness
- dynamic programming
- Interval constrained coloring
- partially ordered set
- protein structure