发表机构
University of Bonn（波恩大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对图编辑距离问题，提出基于分离器的指数时间精确算法，在特定图类上改进了最坏情况运行时间界。
AI 中文摘要
图编辑距离（GED）是一种广泛使用的图相似度度量，要求将一个（带标签）图转换为另一个图所需的最小编辑序列代价，考虑的编辑操作包括节点和边的删除、插入及重新标注。其特殊情况包括图同构问题，以及许多其他要求特定子结构存在或最小代价的图问题，如旅行商问题或最大团问题。我们提出一种新颖的指数时间算法，用于计算精确GED及对应编辑序列，时间复杂度为$O^*(4 + \text{ε})^n$，空间为多项式空间，前提是两个图中的一个存在严格次线性平衡分离器。特别地，若其中一个图是$K_h$-子图自由（例如平面图），或具有有界树宽（GEDLIB中的所有实例均属此类，符合众多实际应用场景），则该时间复杂度成立。这显著改进了这些图类已知的最坏情况运行时间界$O^*(n!)$。
英文摘要
The Graph Edit Distance (GED) is a widely used graph similarity measure asking for the minimum cost of a sequence of edits transforming one (labeled) graph into another. The considered edit operations are deletion, insertion, and relabeling of nodes and edges. Special cases include the Graph Isomorphism problem, as well as many other graph problems that ask for the existence or minimum cost of a certain substructure, like the Traveling Salesman or Maximum Clique problem. We present a novel exponential time algorithm to compute the exact GED and a corresponding edit sequence in $O^*(4 + \varepsilon)^n$ time and polynomial space, provided one of the two graphs admits strictly sublinear balanced separators. In particular, the claimed runtime holds if one of the graphs is $K_h$-minor free (e.g., planar), or has bounded treewidth, which is the case for many real-world applications (e.g., all instances in GEDLIB). This substantially improves the best known worst-case running time bounds of $O^*(n!)$ for these graph classes.
Comments19 pages, 3 figures
