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Parameterized Complexity of Scheduling Problems in Robotic Process Automation

Michal Dvořák, Antonín Novák, Přemysl Šůcha, Dušan Knop, Claire Hanen

TL;DR

The paper investigates the parameterized complexity of single-machine scheduling with precedences, release times, and deadlines in Robotic Process Automation, focusing on chain-like structures, the number of distinct processing times, and time-window patterns. It establishes strong hardness results, including ${W[2]}$-hardness parameterized by the number of chains and para-NP-hardness for combined parameters, along with prec-consistency considerations, while also identifying tractable regimes: a polynomial-time algorithm when all jobs share a single time-window length ($\#(d_j-r_j)=1$), FPT when processing times and times are chain-uniform, and an XP algorithm parameterized by the precedence width $w$. The results illuminate which parameter regimes permit efficient exact solutions and which remain intractable, guiding the design of RPA scheduling algorithms and heuristics. Overall, the work bridges parameterized complexity theory with practical RPA scheduling challenges, offering both theoretical boundaries and actionable strategies for algorithm design.

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.

Parameterized Complexity of Scheduling Problems in Robotic Process Automation

TL;DR

The paper investigates the parameterized complexity of single-machine scheduling with precedences, release times, and deadlines in Robotic Process Automation, focusing on chain-like structures, the number of distinct processing times, and time-window patterns. It establishes strong hardness results, including -hardness parameterized by the number of chains and para-NP-hardness for combined parameters, along with prec-consistency considerations, while also identifying tractable regimes: a polynomial-time algorithm when all jobs share a single time-window length (), FPT when processing times and times are chain-uniform, and an XP algorithm parameterized by the precedence width . The results illuminate which parameter regimes permit efficient exact solutions and which remain intractable, guiding the design of RPA scheduling algorithms and heuristics. Overall, the work bridges parameterized complexity theory with practical RPA scheduling challenges, offering both theoretical boundaries and actionable strategies for algorithm design.

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 . 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.
Paper Structure (23 sections, 7 theorems, 8 equations, 1 figure, 1 table)

This paper contains 23 sections, 7 theorems, 8 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. RPA scheduling model
  3. Related work
  4. Robotic process automation
  5. Scheduling
  6. Parameterized complexity
  7. Contribution and outline
  8. Preliminaries
  9. General notation
  10. Parameterized complexity
  11. Exponential Time Hypothesis
  12. Scheduling
  13. Hardness results
  14. Hardness with prec-consistency
  15. Algorithmic results
  16. ...and 8 more sections

Key Result

Lemma 2

Let $(u_1,u_2,\ldots, u_\ell,v)$ be an instance of Binary Shuffle Product and $\mathcal{I}$ the instance of $1|\operatorname{chains}(k),r_j,d_j|*$ produced by construction:w2hardness. $\mathcal{I}$ is yes-instance if and only if $(u_1,u_2,\ldots,u_{\ell},v)$ is yes-instance.

Figures (1)

  • Figure 1: The structure of the guard jobs in the reduction from \ref{['construction:w2hardness']} for $\Sigma=\{p,q\}=\{1,2\}$ and word $v=122$. The red rectangles represent the time windows $[r_{g_i},d_{g_i})$.

Theorems & Definitions (17)

  • Example 1
  • Lemma 2
  • proof
  • Theorem 3
  • proof
  • Corollary 4
  • Lemma 5
  • proof
  • Claim 1
  • proof
  • ...and 7 more