Generating $k$kk-Hop-Constrained $s$ss-$t$tt Path Graphs

Yuzheng Cai, Siyuan Liu, Weiguo Zheng, Xuemin Lin, Chengbo Zhang, Xuecang Zhang

Abstract: In this paper, we study two different problems that investigate relations between given vertices $s$ and $t$. The first problem is to generate the $k$-hop-constrained $s$-$t$ path graph, i.e., the subgraph consisting of all paths from $s$ to $t$, where each path is not longer than $k$ s.t. $s$ and $t$ appear only once. To solve the first problem, we propose the A-BiBFS$^{++}$t++ method enhanced with the reduced neighbor index and an approximate vertex grouping strategy. The second problem is to generate the $k$-hop-constrained $s$-$t$ simple path graph, i.e., the subgraph consisting of all $k$-hop-constrained simple paths from $s$ to $t$, which is proved to be NP-hard on directed graphs. Based on A-BiBFS$^{++}$t++, we propose the EVE method to tackle the second problem, which exploits the paradigm of edge-wise examination rather than exhaustively enumerating all simple paths. Extensive experiments show that both A-BiBFS$^{++}$s++ and EVE significantly outperform all baselines. 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.