Geometric applications of a matrix searching algorithm
SCG '86 Proceedings of the second annual symposium on Computational geometry
Fibonacci heaps and their uses in improved network optimization algorithms
Journal of the ACM (JACM)
The concave least-weight subsequence problem revisited
Journal of Algorithms
A linear-time algorithm for concave one-dimensional dynamic programming
Information Processing Letters
Sequence comparison with mixed convex and concave costs
Journal of Algorithms
Finding a minimum weight K-link path in graphs with Monge property and applications
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Perspectives of Monge properties in optimization
Discrete Applied Mathematics
Group Testing With DNA Chips: Generating Designs and Decoding Experiments
CSB '03 Proceedings of the IEEE Computer Society Conference on Bioinformatics
Replacing suffix trees with enhanced suffix arrays
Journal of Discrete Algorithms - SPIRE 2002
Efficient Algorithms for the Computational Design of Optimal Tiling Arrays
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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Genomic tiling arrays are a type of DNA microarrays which can investigate the complete genome of arbitrary species for which the sequence is known. The design or selection of suitable oligonucleotide probes for such arrays is however computationally difficult if features such as oligonucleotide quality and repetitive regions are to be considered. We formulate the minimal cost tiling path problem for the selection of oligonucleotides from a set of candidates, which is equivalent to a shortest path problem. An efficient implementation of Dijkstra's shortest path algorithm allows us to compute globally optimal tiling paths from millions of candidate oligonucleotides on a standard desktop computer. The solution to this multi-criterion optimization is spatially adaptive to the problem instance. Our formulation incorporates experimental constraints with respect to specific regions of interest and tradeoffs between hybridization parameters, probe quality and tiling density easily. Solutions for the basic formulation can be obtained more efficiently from Monge theory.