Subadditive Load Balancing

TL;DR

This paper investigates subadditive set functions, introduces a modularization-minimization algorithm with approximation guarantees for load balancing, and empirically evaluates the approach on multi-robot routing tasks.

Contribution

It presents a novel algorithm for subadditive load balancing with theoretical guarantees and a lower bound computation method, applied to multi-robot routing.

Findings

Algorithm achieves provable approximation bounds.

Lower bound technique effectively evaluates solution quality.

Empirical results demonstrate practical applicability in multi-robot routing.

Abstract

Set function optimization is essential in AI and machine learning. We focus on a subadditive set function that generalizes submodularity, and examine the subadditivity of non-submodular functions. We also deal with a minimax subadditive load balancing problem, and present a modularization-minimization algorithm that theoretically guarantees a worst-case approximation factor. In addition, we give a lower bound computation technique for the problem. We apply these methods to the multi-robot routing problem for an empirical performance evaluation.