名义图上的动态规划
Dynamic Programming on Nominal Graphs
摘要：
许多优化问题可以自然地表示为（超）图，其中顶点对应于变量，边对应于任务，其成本取决于相邻变量的值。利用图的结构，合适的动态规划策略可以选择变量的评估的某些顺序，其保证达到最优解和在优化过程中计算的表的最小尺寸。本文引入了一个简单的具有平行合成和限制的代数规格说明，其结构公理的项是上述图。此外，自由（不受限制）的顶点被标记为变量，规范包括有限支持的名称置换操作。我们展示了著名的树分解图和我们的术语之间的对应关系。如果删除作用域扩展的公理，那么几个（层次）术语实际上对应于同一个图。可以找到对应于每个层次术语的合适的图形结构。在某些目标代数中评估这样的图形结构产生动态规划策略。如果目标代数满足作用域扩展公理，则结果不依赖于特定的结构，而仅依赖于原始图。我们将我们的方法应用于ASCENS电动汽车案例研究中开发的停车优化问题，与大众汽车合作。动态规划评估对于自主系统来说特别有趣，在自主系统中，实际行为通常包括传播局部知识以获得全局知识并将其带回用于局部决策。
英文摘要：
Many optimization problems can be naturally represented as (hyper) graphs, where vertices correspond to variables and edges to tasks, whose cost depends on the values of the adjacent variables. Capitalizing on the structure of the graph, suitable dynamic programming strategies can select certain orders of evaluation of the variables which guarantee to reach both an optimal solution and a minimal size of the tables computed in the optimization process. In this paper we introduce a simple algebraic specification with parallel composition and restriction whose terms up to structural axioms are the graphs mentioned above. In addition, free (unrestricted) vertices are labelled with variables, and the specification includes operations of name permutation with finite support. We show a correspondence between the well-known tree decompositions of graphs and our terms. If an axiom of scope extension is dropped, several (hierarchical) terms actually correspond to the same graph. A suitable graphical structure can be found, corresponding to every hierarchical term. Evaluating such a graphical structure in some target algebra yields a dynamic programming strategy. If the target algebra satisfies the scope extension axiom, then the result does not depend on the particular structure, but only on the original graph. We apply our approach to the parking optimization problem developed in the ASCENS e-mobility case study, in collaboration with Volkswagen. Dynamic programming evaluations are particularly interesting for autonomic systems, where actual behavior often consists of propagating local knowledge to obtain global knowledge and getting it back for local decisions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
