Improved Approximation Algorithms for NMR Spectral Peak Assignment

Abstract

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 u _i+1 follows u _i in U and if v _j+1 follows v _j in V, then u _i is matched with v _j if and only if u _i+1 is matched with v _j+1. The problem has recently been formulated as a crucial step in an algorithmic approach for interpreting NMR spectral data [15]. 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 [15]. We first propose a 2-approximation algorithm for the problem, which follows directly from the recent result of Bar-Noy et al. [2] on interval scheduling. However, our extensive experimental results on real NMR spectral data illustrate that the algorithm performs poorly in terms of recovering the target-matching (i.e. correct) edges. We then propose another approximation algorithm that tries to take advantage

Supported in part by the Grant-in-Aid for Scientific Research of the Ministry of Education, Science, Sports and Culture of Japan, under Grant No. 12780241. Part of the work done while visiting at UC Riverside.

Supported in part by a UCR startup grant and NSF Grants CCR-9988353 and ITR-0085910.

Supported in part by NSERC grants RGPIN249633 and A008599, and Startup Grant REE-P5-01-02-Sci from the University of Alberta.

Supported by NSF Grant CCR-9988353.

Supported by the Office of Biological and Environmental Research, U.S. Department of Energy, under Contract DE-AC05-00OR22725, managed by UT-Battelle, LLC.