arXiv subjects

Rick S. H. Willemsen

Publications and source records attributed to Rick S. H. Willemsen.

3 recordsLinked to original sources

arXiv2026

Exact and Efficient Methods for Identifying Carcinogenic Multi-Hit Gene Combinations

Cancer is driven by an estimated two to nine gene mutations, known as multi-hit combinations. Due to the large number of genes, identifying these multi-hit combinations presents a computationally challenging problem, which has previously required supercomputers to enumerate all or most gene combinations. Recent work formulated this classification task as the Multi-Hit Cancer Driver Set Cover Problem (MHCDSCP) and solved it via column generation on a single commodity CPU, where a pricing problem identifies promising gene combinations (arXiv:2602.22551). The main bottleneck is the pricing problem that has to be solved repeatedly. To solve the pricing problem to optimality, we propose a dedicated depth first search method that enumerates all possible gene combinations. Although enumerating gene combinations with depth first search have been performed on supercomputers with around 150,000 CPU cores (arXiv:2603.16721), our depth first search algorithm solves the pricing problem to optimality within seconds on a single CPU by leveraging dual information to prune large parts of the search space. By eliminating this bottleneck, our approach yields the first exact method for the MHCDSCP, which is guaranteed to find a global optimal solution.

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arXiv2026

Identifying Multi-Hit Cancer Drivers Without Massive Parallelization: A CP, MIP, and Column Generation Framework

Cancer is often driven by specific combinations of an estimated two to nine gene mutations, known as multi-hit combinations. Identifying these multi-hit combinations of gene mutations that drive cancer is critical for understanding carcinogenesis and designing targeted therapies. We formalize this challenge as the Multi-Hit Cancer Driver Set Cover Problem (MHCDSCP), optimizing the selection of gene combinations to maximize tumor coverage while strictly minimizing normal sample misclassification. While existing approaches rely on exhaustive enumeration and massive parallelization, we introduce fast heuristics based on constraint programming and mixed integer programming formulations. Evaluated on real-world cancer genomics data, our framework matches state-of-the-art supercomputing methods using a single commodity CPU in under a minute. We also propose a price-and-branch heuristic which, by solving the root node to optimality, provides the first provably optimal solutions for over half of the benchmark instances, thereby verifying the near-optimality of our fast heuristics. These findings demonstrate that on real-world problem instances, the MHCDSCP is far less computationally demanding than previously believed, providing an accessible baseline that enables the exploration of previously intractable multi-hit modeling assumptions.

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arXiv2025

Generating Random Vectors satisfying Linear and Nonlinear Constraints

We consider the problem of generating n-dimensional vectors with a fixed sum, with the goal of generating a uniform distribution of vectors over a valid region. This means that each possible vector has an equal probability of being generated. The Dirichlet-Rescale (DRS) algorithm, introduced by Griffin et al. (2020), aims to generate a uniform distribution of vectors with fixed sum that satisfies lower and upper bounds on the individual entries. However, we demonstrate that the uniform distribution property of the DRS algorithm does not hold in general. Using an analytical procedure and a statistical test, we show that the vectors generated by the DRS algorithm do not appear to be drawn from a uniform distribution. To resolve this issue, we propose the Dirichlet-Rescale-Constraints (DRSC) algorithm, which handles more general constraints, including both linear and nonlinear constraints, while ensuring that the vectors are drawn from a uniform distribution. In our computational experiments we demonstrate the effectiveness of the DRSC algorithm.

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