A Fast and Practical Column Generation Approach for Identifying Carcinogenic Multi-Hit Gene Combinations

2026-02-25

AI Summary

This study addresses the challenge of identifying combinatorial multi-gene mutation patterns that drive cancer by formulating it as a Multi-Hit Cancer Driver Set Cover Problem (MHCDSCP), which seeks to maximize coverage of tumor samples while minimizing coverage of normal samples. To solve this computationally demanding problem, the authors propose a column-generation heuristic algorithm grounded in constraint programming and mixed-integer programming, substantially reducing computational complexity. The method achieves state-of-the-art performance on real cancer genomics data, delivering results comparable to existing top-tier approaches while requiring only a standard CPU and completing computations within one minute. Notably, it obtains provably optimal solutions on small-scale instances, thereby overcoming the traditional reliance on high-performance computing resources for such problems.

Technology Category

• Search and Optimization: Combinatorial Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Multi-instance/Multi-view Learning

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Economics, Online Markets and Human Computation: Research challenges in human and human-AI computation
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Cancer is often driven by specific combinations of an estimated two to nine gene mutations, known as multi-hit combinations. Identifying these combinations is critical for understanding carcinogenesis and designing targeted therapies. We formalise this challenge as the Multi-Hit Cancer Driver Set Cover Problem (MHCDSCP), a binary classification problem that selects gene combinations to maximise coverage of tumor samples while minimising coverage of normal samples. Existing approaches typically rely on exhaustive search and supercomputing infrastructure. In this paper, we present constraint programming and mixed integer programming formulations of the MHCDSCP. Evaluated on real-world cancer genomics data, our methods achieve performance comparable to state-of-the-art methods while running on a single commodity CPU in under a minute. Furthermore, we introduce a column generation heuristic capable of solving small instances to optimality. These results suggest that solving the MHCDSCP is less computationally intensive than previously believed, thereby opening research directions for exploring modelling assumptions.

Problem

• multi-hit gene combinations
• carcinogenesis
• cancer driver identification
• set cover problem
• tumor genomics

Innovation

• column generation
• multi-hit gene combinations
• mixed integer programming
• constraint programming
• cancer driver identification