Maximum bounded 3-dimensional matching is MAX SNP-complete
Information Processing Letters
Smallest-last ordering and clustering and graph coloring algorithms
Journal of the ACM (JACM)
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
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We consider the task of SNP (Single Nucleotide Polymorphism) genotyping. In many studies, genotyping of a large number of SNPs must be performed. Multiple SNPs can be genotyped together in the same assay (a process called multiplexed genotyping) provided they adhere to some constraints. We address the optimization problem of designing assays that maximize the number of genotyped SNPs, subject to the multiplexing constraints. We focus on the SNP genotyping method based on primer extension and mass-spectrometry (PEA/MS). We translate the optimization problem to a graph coloring problem, and provide essentially optimal heuristics for solving the corresponding coloring problem. In addition, we consider a method that enables a dramatic increase in the multiplexing rate by modifying primer masses. In this case, the multiplexing design problem can be modelled as a matching problem in hypergraphs. We analyze both theoretical and practical aspects of the problem, providing hardness results and practical heuristics. The heuristics are tested using simulation methods, and prove to be close to optimal in practice.