Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Dependent rounding and its applications to approximation algorithms
Journal of the ACM (JACM)
Broadcast scheduling: algorithms and complexity
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Computing H/D-exchange speeds of single residues from data of peptic fragments
Proceedings of the 2008 ACM symposium on Applied computing
A Fast Algorithm for Enumerating Bipartite Perfect Matchings
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
A quasi-PTAS for profit-maximizing pricing on line graphs
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Deconstructing Intractability: A Case Study for Interval Constrained Coloring
CPM '09 Proceedings of the 20th Annual Symposium on Combinatorial Pattern Matching
Deconstructing intractability-A multivariate complexity analysis of interval constrained coloring
Journal of Discrete Algorithms
Upper and lower bounds for finding connected motifs in vertex-colored graphs
Journal of Computer and System Sciences
The interval constrained 3-coloring problem
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Constraint satisfaction problems: convexity makes all different constraints tractable
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
Constraint satisfaction problems: Convexity makes AllDifferent constraints tractable
Theoretical Computer Science
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We consider the interval constrained coloringproblem, which appears in the interpretation of experimental data in biochemistry. Monitoring hydrogen-deuterium exchange rates via mass spectroscopy experiments is a method used to obtain information about protein tertiary structure. The output of these experiments provides data about the exchange rate of residues in overlapping segments of the protein backbone. These segments must be re-assembled in order to obtain a global picture of the protein structure. The interval constrained coloringproblem is the mathematical abstraction of this re-assembly process.The objective of the interval constrained coloring problem is to assign a color (exchange rate) to a set of integers (protein residues) such that a set of constraints is satisfied. Each constraint is made up of a closed interval (protein segment) and requirements on the number of elements that belong to each color class (exchange rates observed in the experiments).We show that the problem is NP-complete for arbitrary number of colors and we provide algorithms that given a feasible instance find a coloring that satisfies all the coloring requirements within ±1 of the prescribed value. In light of our first result, this is essentially the best one can hope for. Our approach is based on polyhedral theory and randomized rounding techniques. Furthermore, we develop a quasi-polynomial-time approximation scheme for a variant of our problem where we are asked to find a coloring satisfying as many fragments as possible.