The power of geometric duality
BIT - Ellis Horwood series in artificial intelligence
Rapid dynamic programming algorithms for RNA secondary structure
Advances in Applied Mathematics
Geometric applications of a matrix searching algorithm
SCG '86 Proceedings of the second annual symposium on Computational geometry
Applications of random sampling in computational geometry, II
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
An almost linear time algorithm for generalized matrix searching
SIAM Journal on Discrete Mathematics
Solving query-retrieval problems by compacting Voronoi diagrams
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Reporting points in halfspaces
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Sparse dynamic programming I: linear cost functions
Journal of the ACM (JACM)
Sparse dynamic programming II: convex and concave cost functions
Journal of the ACM (JACM)
Perspectives of Monge properties in optimization
Discrete Applied Mathematics
Halfspace range search: an algorithmic application of K-sets
SCG '85 Proceedings of the first annual symposium on Computational geometry
A linear space algorithm for computing maximal common subsequences
Communications of the ACM
Dynamic Programming and Optimal Control
Dynamic Programming and Optimal Control
Optimal Histograms with Quality Guarantees
VLDB '98 Proceedings of the 24rd International Conference on Very Large Data Bases
Efficient dynamic programming using quadrangle inequalities
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
Dynamic Programming
Hidden Markov models approach to the analysis of array CGH data
Journal of Multivariate Analysis
Using penalized contrasts for the change-point problem
Signal Processing
Quantile smoothing of array CGH data
Bioinformatics
Approximation and streaming algorithms for histogram construction problems
ACM Transactions on Database Systems (TODS)
Speeding up dynamic programming
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Dynamic half-space reporting, geometric optimization, and minimum spanning trees
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
The Knuth-Yao quadrangle-inequality speedup is a consequence of total monotonicity
ACM Transactions on Algorithms (TALG)
GIMscan: a new statistical method for analyzing whole-genome array CGH data
RECOMB'07 Proceedings of the 11th annual international conference on Research in computational molecular biology
Efficient calculation of interval scores for DNA copy number data analysis
RECOMB'05 Proceedings of the 9th Annual international conference on Research in Computational Molecular Biology
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The development of cancer is largely driven by the gain or loss of subsets of the genome, promoting uncontrolled growth or disabling defenses against it. Denoising array-based Comparative Genome Hybridization (aCGH) data is an important computational problem central to understanding cancer evolution. In this article, we propose a new formulation of the denoising problem that we solve with a “vanilla” dynamic programming algorithm, which runs in O(n2) units of time. Then, we propose two approximation techniques. Our first algorithm reduces the problem into a well-studied geometric problem, namely halfspace emptiness queries, and provides an ε additive approximation to the optimal objective value in Õ(n&frac43;+δ log (&fracU;ε)) time, where δ is an arbitrarily small positive constant and U = max{&sqrtC;,(|Pi|) i=1,…,n} (P=(P1, P2, …, Pn), Pi ∈ ℝ, is the vector of the noisy aCGH measurements, C a normalization constant). The second algorithm provides a (1 ± ε) approximation (multiplicative error) and runs in O(n log n/ε) time. The algorithm decomposes the initial problem into a small (logarithmic) number of Monge optimization subproblems that we can solve in linear time using existing techniques. Finally, we validate our model on synthetic and real cancer datasets. Our method consistently achieves superior precision and recall to leading competitors on the data with ground truth. In addition, it finds several novel markers not recorded in the benchmarks but supported in the oncology literature.