工作流可满足性问题的模式回溯算法
Pattern Backtracking Algorithm for the Workflow Satisfiability Problem
摘要：
工作流可满足性问题（WSP）询问是否存在授权用户到工作流规范中的步骤的分配，并受到分配上的某些约束。(Such一个赋值被称为有效。）这个问题是NP难的，即使限制到大类的用户独立的约束。由于步骤$k$的数量在实践中相对较小，因此自然考虑通过$k$对WSP进行参数化。我们提出了一个新的固定参数算法来解决WSP与用户无关的约束。我们的方法中的分配被划分为等价类，使得类的数量仅在$k$中是指数的。我们表明，可以决定，在多项式时间，是否有一个有效的分配在一个等价类。通过利用这个属性，我们的算法减少了搜索空间的等价类，它浏览的回溯框架内的空间，因此成为一个有效的，但相对简单的实现或概括的解决方案的方法。我们的经验评估我们的算法对国家的最先进的方法，并表明，它显然赢得了我们的测试问题的整个范围内的竞争，并显着扩展域的实际可解决的WSP的实例。
英文摘要：
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.
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