PALMA: A Lightweight Tropical Algebra Library for ARM-Based Embedded Systems

TL;DR

PALMA is a lightweight, open-source C library that implements tropical algebra on ARM-based embedded systems, enabling efficient optimization for real-time applications like UAV control and IoT routing.

Contribution

It introduces PALMA, the first dependency-free tropical algebra library optimized for ARM embedded platforms, supporting multiple semirings and SIMD acceleration.

Findings

Achieves peak performance of 2,274 MOPS on Raspberry Pi 4.

Provides up to 11.9x speedup over Bellman-Ford.

Enables sub-10 microsecond scheduling in real-time workloads.

Abstract

Tropical algebra, including max-plus, min-plus, and related idempotent semirings, provides a unifying framework in which many optimization problems that are nonlinear in classical algebra become linear. This property makes tropical methods particularly well suited for shortest paths, scheduling, throughput analysis, and discrete event systems. Despite their theoretical maturity and practical relevance, existing tropical algebra implementations primarily target desktop or server environments and remain largely inaccessible on resource-constrained embedded platforms, where such optimization problems are most acute. We present PALMA (Parallel Algebra Library for Max-plus Applications), a lightweight, dependency-free C library that brings tropical linear algebra to ARM-based embedded systems. PALMA implements a generic semiring abstraction with SIMD-accelerated kernels, enabling a single computational framework to support shortest paths, bottleneck paths, reachability, scheduling, and throughput analysis. The library supports five tropical semirings, dense and sparse (CSR) representations, tropical closure, and spectral analysis via maximum cycle mean computation. We evaluate PALMA on a Raspberry Pi 4 and demonstrate peak performance of 2,274 MOPS, speedups of up to 11.9 times over classical Bellman-Ford for single-source shortest paths, and sub-10 microsecond scheduling solves for real-time control workloads. Case studies in UAV control, IoT routing, and manufacturing systems show that tropical algebra enables efficient, predictable, and unified optimization directly on embedded hardware. PALMA is released as open-source software under the MIT license.