Exact Algorithms for Resource Reallocation Under Budgetary Constraints

TL;DR

This paper introduces the R-BR problem, a resource reallocation challenge under budget constraints, and provides three efficient exact algorithms suitable for various network topologies, advancing both practical and theoretical aspects.

Contribution

The paper formulates the R-BR problem and develops three fixed-parameter tractable algorithms tailored for specific network structures, enhancing resource reallocation methods.

Findings

Algorithms scale well with input size.

Effective for rural, transportation, and complex networks.

Bridges practical and theoretical resource allocation challenges.

Abstract

Efficient resource (re-)allocation is a critical challenge in optimizing productivity and sustainability within multi-party supply networks. In this work, we introduce the \textsc{Red-Blue Reinforcement} (R-BR) problem, where a service provider under budgetary constraints must minimize client reallocations to reduce the required number of servers they should maintain by a specified amount. We conduct a systematic algorithmic study, providing three exact algorithms that scale well as the input grows (FPT), which could prove useful in practice. Our algorithms are efficient for topologies that model rural road networks (bounded distance to cluster), modern transportation systems (bounded modular-width), or have bounded clique-width, a parameter that is of great theoretical importance.