Pattern Backtracking Algorithm for the Workflow Satisfiability Problem

TL;DR

This paper introduces a fixed-parameter backtracking algorithm for the workflow satisfiability problem that efficiently handles user-independent constraints by exploiting equivalence classes, significantly improving practical solvability.

Contribution

The authors develop a novel fixed-parameter algorithm based on equivalence class partitioning, enhancing the efficiency of solving the WSP with user-independent constraints.

Findings

Outperforms existing methods on benchmark problems

Extends the range of practically solvable WSP instances

Reduces search space via equivalence class partitioning

Abstract

The workflow satisfiability problem (WSP) asks whether there exists an assignment of authorised users to the steps in a workflow specification, subject to certain constraints on the assignment. (Such an assignment is called valid.) The problem is NP-hard even when restricted to the large class of user-independent constraints. Since the number of steps $k$ is relatively small in practice, it is natural to consider a parametrisation of the WSP by $k$. We propose a new fixed-parameter algorithm to solve the WSP with user-independent constraints. The assignments in our method are partitioned into equivalence classes such that the number of classes is exponential in $k$ only. We show that one can decide, in polynomial time, whether there is a valid assignment in an equivalence class. By exploiting this property, our algorithm reduces the search space to the space of equivalence classes, which it browses within a backtracking framework, hence emerging as an efficient yet relatively simple-to-implement or generalise solution method. We empirically evaluate our algorithm against the state-of-the-art methods and show that it clearly wins the competition on the whole range of our test problems and significantly extends the domain of practically solvable instances of the WSP.