Formal Primal-Dual Algorithm Analysis

2026-04-22

AI Summary

This work addresses the absence of a mechanized formal verification framework for primal-dual algorithm analysis. It presents the first systematic formalization in Isabelle/HOL that supports rigorous correctness and performance verification of such algorithms, unifying a diverse range of instances—from the classical Hungarian algorithm to modern Adwords algorithms—within a single coherent framework. By achieving machine-checked proofs for multiple primal-dual algorithms, this study not only establishes their formal correctness but also develops a reusable library of verified components. The resulting infrastructure offers a novel paradigm for trustworthy verification of combinatorial optimization algorithms, enhancing both reliability and reusability in formal methods applied to algorithmic analysis.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Combinatorial Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

We present an ongoing effort to build a framework and a library in Isabelle/HOL for formalising primal-dual arguments for the analysis of algorithms. We discuss a number of example formalisations from the theory of matching algorithms, covering classical algorithms like the Hungarian Method, widely considered the first primal-dual algorithm, and modern algorithms like the Adwords algorithm, which models the assignment of search queries to advertisers in the context of search engines.

Problem

• primal-dual
• formal verification
• algorithm analysis
• Isabelle/HOL
• matching algorithms

Innovation

• formal verification
• primal-dual algorithms
• Isabelle/HOL
• matching algorithms
• algorithm analysis