A common parallel framework for LLP combinatorial problems

TL;DR

This paper introduces LLP-FW, a universal lock-free framework for solving a wide range of combinatorial optimization problems efficiently by leveraging lattice-linear predicates, simplifying parallel algorithm development.

Contribution

The paper presents LLP-FW, a general lock-free runtime that handles multiple combinatorial problems with minimal problem-specific code, unifying and simplifying parallel solutions.

Findings

LLP-FW effectively solves diverse combinatorial problems.

It compares favorably with custom solutions in most cases.

The framework reduces problem-specific implementation effort.

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.