面向生成跳数约束的 s-t 简单路径图
Towards Generating Hop-constrained s-t Simple Path Graphs
AI总结：
本文研究 k 跳约束 s-t 简单路径图生成问题，证明其在有向图上 NP 困难，并提出基于逐边检查和必要顶点的 EVE 算法，在真实网络上显著优于基线且可加速现有路径枚举方法。
摘要：
图已广泛应用于现实世界的各类应用中，在这些应用里，研究顶点之间的关系是一项重要任务。本文研究生成 k 跳约束的 s-t 简单路径图的问题，即由从顶点 s 到顶点 t、长度不超过 k 的所有简单路径组成的子图。据我们所知，我们首次形式化了该问题，并证明了其在有向图上的 NP 困难性。为应对这一具有挑战性的问题，我们提出了一种名为 EVE 的高效算法，该算法采用逐边检查的范式，而不是穷举枚举所有路径。借助出现在顶点对之间所有简单路径中的必要顶点，EVE 区分出必定包含（或必定不包含）在目标简单路径图中的边，并以 O(k^2|E|) 的时间代价生成一个紧上界图。每条剩余的未确定边会被进一步验证，以给出精确答案。我们在 15 个真实网络上进行了大量实验。结果表明，EVE 显著优于所有基线方法，性能提升达数个数量级。此外，通过将 EVE 作为内置模块，当前最先进的跳数约束简单路径枚举方法最多可加速一个数量级。
英文摘要：
Graphs have been widely used in real-world applications, in which investigating relations between vertices is an important task. In this paper, we study the problem of generating the k-hop-constrained s-t simple path graph, i.e., the subgraph consisting of all simple paths from vertex s to vertex t of length no larger than k. To our best knowledge, we are the first to formalize this problem and prove its NP-hardness on directed graphs. To tackle this challenging problem, we propose an efficient algorithm named EVE, which exploits the paradigm of edge-wise examination rather than exhaustively enumerating all paths. Powered by essential vertices appearing in all simple paths between vertex pairs, EVE distinguishes the edges that are definitely (or not) contained in the desired simple path graph, producing a tight upper-bound graph in the time cost $\mathcal{O}(k^2|E|)$. Each remaining undetermined edge is further verified to deliver the exact answer. Extensive experiments are conducted on 15 real networks. The results show that EVE significantly outperforms all baselines by several orders of magnitude. Moreover, by taking EVE as a built-in block, state-of-the-art for hop-constrained simple path enumeration can be accelerated by up to an order of magnitude.
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。
