A Faster Deterministic Algorithm for Kidney Exchange via Representative Set

2026-03-19

AI Summary

This work addresses the combinatorial optimization challenge of maximizing successful kidney transplants under limited medical resources and constraints on cycle and chain lengths in kidney exchange programs. For the first time, the authors introduce the representative set technique to this domain, integrating it with parameterized algorithm design and graph-theoretic methods to develop a novel deterministic algorithm. The proposed approach substantially improves upon the best-known time complexity upper bound, reducing it from $O^*(14.34^t)$ to $O^*(6.855^t)$, thereby significantly enhancing computational efficiency for solving large-scale instances of the problem.

Technology Category

• Search and Optimization: Combinatorial Optimization
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

The Kidney Exchange Problem is a prominent challenge in healthcare and economics, arising in the context of organ transplantation. It has been extensively studied in artificial intelligence and optimization. In a kidney exchange, a set of donor-recipient pairs and altruistic donors are considered, with the goal of identifying a sequence of exchange -- comprising cycles or chains starting from altruistic donors -- such that each donor provides a kidney to the compatible recipient in the next donor-recipient pair. Due to constraints in medical resources, some limits are often imposed on the lengths of these cycles and chains. These exchanges create a network of transplants aimed at maximizing the total number, $t$, of successful transplants. Recently, this problem was deterministically solved in $O^*(14.34^t)$ time (IJCAI 2024). In this paper, we introduce the representative set technique for the Kidney Exchange Problem, showing that the problem can be deterministically solved in $O^*(6.855^t)$ time.

Problem

• Kidney Exchange
• Transplantation
• Optimization
• Cycles and Chains
• Resource Constraints

Innovation

• Kidney Exchange
• Representative Set
• Deterministic Algorithm
• Parameterized Complexity
• Optimization