Representations of task assignments in distributed systems using Young tableaux and symmetric groups

TL;DR

This paper introduces a novel method using Young tableaux and symmetric groups to represent task assignments in distributed systems, enhancing expressiveness without focusing on optimization.

Contribution

It proposes a new tableau-based representation for task and agent partitions in distributed systems, leveraging combinatorics and group theory.

Findings

Enhanced expressiveness of task representations

Framework for representing partitioned agents and tasks

Potential for improved analysis of task assignments

Abstract

This paper presents a novel approach to representing task assignments for partitioned agents (respectively, tasks) in distributed systems. A partition of agents (respectively, tasks) is represented by a Young tableau, which is one of the main tools in studying symmetric groups and combinatorics. In this paper we propose a task, agent, and assignment tableau in order to represent a task assignment for partitioned agents (respectively, tasks) in a distributed system. This paper is concerned with representations of task assignments rather than finding approximate or near optimal solutions for task assignments. A Young tableau approach allows us to raise the expressiveness of partitioned agents (respectively, tasks) and their task assignments.