Introduction to algorithms
Maximum bounded 3-dimensional matching is MAX SNP-complete
Information Processing Letters
Approximating discrete collections via local improvements
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Greedy local improvement and weighted set packing approximation
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
A unified approach to approximating resource allocation and scheduling
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Computing in Science and Engineering
An Efficient Branch-and-Bound Algorithm for the Assignment of Protein Backbone NMR Peaks
CSB '02 Proceedings of the IEEE Computer Society Conference on Bioinformatics
Automated Protein NMR Resonance Assignments
CSB '03 Proceedings of the IEEE Computer Society Conference on Bioinformatics
CSB '05 Proceedings of the 2005 IEEE Computational Systems Bioinformatics Conference
An approximation algorithm for a bottleneck traveling salesman problem
Journal of Discrete Algorithms
An approximation algorithm for a bottleneck traveling salesman problem
CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
RIBRA–an error-tolerant algorithm for the NMR backbone assignment problem
RECOMB'05 Proceedings of the 9th Annual international conference on Research in Computational Molecular Biology
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We study a constrained bipartite matching problem where the input is a weighted bipartite graph G = (U, V, E), U is a set of vertices following a sequential order, V is another set of vertices partitioned into a collection of disjoint subsets, each following a sequential order, and E is a set of edges between U and V with non-negative weights. The objective is to find a matching in G with the maximum weight that satisfies the given sequential orders on both U and V, i.e. if ui+1 follows ui in U and if Vj+1 follows vj in V, then ui is matched with vj if and only if ui+1 is matched with vj+1. The problem has recently been formulated as a crucial step in an algorithmic approach for interpreting NMR spectral data (IEEE Comput Sci. Eng. 4 (2002) 50-62). The interpretation of NMR spectral data is known as a key problem in protein structure determination via NMR spectroscopy. Unfortunately, the constrained bipartite matching problem is NP-hard (IEEE Comput. Sci. Eng. 4 (2002) 50-62). We first propose a 2-approximation algorithm for the problem, which follows directly from the recent result of Bar-Noy et al. (Proc. 32nd ACM Symp. on Theory of Computing (STOC'00), 2000, pp. 735 -744) on interval scheduling. However, our extensive experimental results on real NMR spectral data illustrate that the algorithm perform poorly in terms of recovering target-matching edges. We then propose another approximation algorithm that tries to take advantage of the "density" of the sequential order information in V. Although we are only able to prove an approximation ratio of 3 log2D for this algorithm, where D is the length of a longest string in V, the experimental results demonstrate that this new algorithm performs much better on real data, i.e. it is able to recover a large fraction of target-matching edges and the weight of its output matching is often in fact close to the maximum. We also prove that the problem is MAX SNP-hard, even if the input bipartite graph is unweighted. We further present an approximation algorithm for a nontrivial special case that breaks the ratio 2 barrier.