Parameterized Complexity of Scheduling Problems in Robotic Process Automation

TL;DR

This paper analyzes the parameterized complexity of a scheduling problem in Robotic Process Automation, revealing hardness results and identifying conditions for polynomial-time and fixed-parameter tractable algorithms.

Contribution

It provides the first complexity analysis of RPA scheduling problems, establishing hardness results and developing algorithms for specific parameter settings.

Findings

W[2]-hardness with respect to the number of chains

Polynomial-time algorithm when all jobs share a single time-window length

FPT algorithm when processing times, release times, and deadlines are chain-uniform

Abstract

This paper studies the growing domain of Robotic Process Automation (RPA) problems. Motivated by scheduling problems arising in RPA, we study the parameterized complexity of the single-machine problem $1|\text{prec},r_j,d_j|*$. We focus on parameters naturally linked to RPA systems, including chain-like precedences, the number of distinct processing times, and the structure of the time windows. We show that the problem is W[2]-hard parameterized by the number of chains, even with only two prescribed processing times and two distinct time-window lengths. This hardness remains even for distinct processing times and time windows under prec-consistent time windows. On the positive side, we obtain polynomial-time algorithm when all jobs share a single time-window length and FPT when the processing times, release times and deadlines are chain-uniform. We also show that the problem lies in XP when parameterized by the width of the precedence relation.