图同构问题的物理动力学算法
Physically-motivated dynamical algorithms for the graph isomorphism problem
摘要：
我们研究经典和量子物理为基础的算法来解决图同构问题。我们的工作整合和扩展了Gudkov等人（cond-mat/0209112）和Rudolph（quant-ph/0206068）的先前工作。Gudkov等人提出了一种算法，旨在通过模仿经典的动态多粒子过程来在多项式时间内解决图同构问题。我们表明，该算法无法区分对非同构强正则图，从而提供了一个无限类的反例。我们还表明，最简单的量子推广的算法也失败了。然而，通过结合Gudkov et al.的算法与Rudoph提出的建设，其中一个检查一个图形描述的动力学两个粒子的原始图形，我们发现一个算法，成功地区分所有对非同构强正则图，我们测试（最多29个顶点）。
英文摘要：
We investigate classical and quantum physics-based algorithms for solving the graph isomorphism problem. Our work integrates and extends previous work by Gudkov et al. (cond-mat/0209112) and by Rudolph (quant-ph/0206068). Gudkov et al. propose an algorithm intended to solve the graph isomorphism problem in polynomial time by mimicking a classical dynamical many-particle process. We show that this algorithm fails to distinguish pairs of non-isomorphic strongly regular graphs, thus providing an infinite class of counterexamples. We also show that the simplest quantum generalization of the algorithm also fails. However, by combining Gudkov et al.'s algorithm with a construction proposed by Rudoph in which one examines a graph describing the dynamics of two particles on the original graph, we find an algorithm that successfully distinguishes all pairs of non-isomorphic strongly regular graphs that we tested (with up to 29 vertices).
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。
