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Selecting Chromosomes for Polygenic Traits: Algorithms and Complexity

Author Or Zuk

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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Combinatorial optimization
  • Applied computing → Computational genomics
  • Applied computing → Computational genomics
Keywords
  • polygenic scores
  • combinatorial optimization
  • genomic block selection
  • NP-hardness
  • semidefinite programming
  • synthetic genomics

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Abstract

We define and study the problem of genomic block selection for multiple complex traits. In this problem, one constructs a genome by selecting different genomic parts (e.g. chromosomes) from different source genomes. The constructed genome is associated with a vector of polygenic scores, obtained by summing the polygenic scores of the different genomic parts, and the goal is to minimize a given loss function of this vector. The problem is motivated by several emerging technologies: chromosome substitution lines in crop breeding, where chromosomal segments from wild relatives are combined to improve polygenic traits such as yield and stress tolerance; chromosome transfer between yeast strains for optimizing complex industrial phenotypes; and chromosomal transplantation technologies in mammalian cells. We suggest and study several natural loss functions relevant for both quantitative and threshold traits, and show that the problem is NP-complete even for a single trait and two copies, yet only weakly so, being pseudo-polynomially solvable for any fixed number of traits. We propose three algorithms with complementary roles: a Branch-and-Bound algorithm that returns the certified global optimum for any monotone loss, a fast Block-Coordinate-Descent (BCD) heuristic with random restarts that applies to any loss, and a semidefinite-programming (SDP) relaxation that provides a certified lower bound on the optimal loss for quadratic losses, and hence an optimality-gap bound when paired with the BCD solution - empirically tight in our experiments. Using the infinitesimal model for genetic architecture, we further derive, for linear losses, a closed-form approximation for the expected gain of block selection relative to random selection across multiple traits. On yeast-scale simulations BCD matches the certified Branch-and-Bound optimum on 100% of threshold-loss instances at 466× the speed, attains a certified optimality gap of at most ≈10% of the SDP lower bound for stabilizing-loss instances, and the realized gain roughly matches the analytic prediction.

Cite As Get BibTex

Or Zuk. Selecting Chromosomes for Polygenic Traits: Algorithms and Complexity. In 26th International Conference on Algorithms for Bioinformatics (WABI 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 390, pp. 28:1-28:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.WABI.2026.28

Author Details

Or Zuk
  • Department of Statistics and Data Science, The Hebrew University of Jerusalem, Israel

Funding

Supported by the Israeli Science Foundation (grants #2830/20 and #2392/22).

Supplementary Materials

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