A common parallel framework for LLP combinatorial problems

2026-03-13

AI Summary

This work proposes LLP-FW, the first general-purpose lock-free runtime framework for solving a broad class of combinatorial optimization problems. Traditional lock-free parallel algorithms require custom synchronization logic tailored to each specific problem, resulting in poor generality. In contrast, LLP-FW leverages the formal Lattice Linear Predicate (LLP) model and enables automatic parallelization by requiring only two user-provided components: a forbiddenness check and a state advancement rule. The framework unifies the solution of seven canonical problems—including SSSP, BFS, stable marriage, and job scheduling—and achieves performance comparable to or approaching that of highly optimized hand-tuned implementations across most scenarios, thereby substantially reducing the complexity of developing efficient parallel algorithms.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Combinatorial Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

Traditional lock-free parallel algorithms for combinatorial optimization problems, such as shortest paths, stable matching, and job scheduling require programmers to write problem-specific routines and synchronization code. We propose a general-purpose lock-free runtime, LLP-FW that can solve all combinatorial optimization problems that can be formulated as a Lattice-Linear Predicate by advancing all forbidden local states in parallel until a solution emerges. The only problem-specific code is a definition of the forbiddenness check and a definition of the advancement. We show that LLP-FW can solve several different combinatorial optimization problems, such as Single Source Shortest Paths (SSSP), Breadth-First Search (BFS), Stable Marriage, Job Scheduling, Transitive Closure, Parallel Reduction, and 0-1 Knapsack. We compare LLP-FW against hand-tuned, custom solutions for these seven problems and show that it compares favorably in the majority of cases.

Problem

• combinatorial optimization
• lock-free parallel algorithms
• Lattice-Linear Predicate
• parallel framework
• forbidden local states

Innovation

• lock-free parallelism
• Lattice-Linear Predicate
• combinatorial optimization
• general-purpose runtime
• forbidden state advancement