In this paper, we investigate the problem of determining $s-t$ reachability in choice networks. In the traditional $s-t$ reachability problem, we are given a weighted network tuple $\mathbf{G}=〈V,E,\mathbf{c},s,t〉$, with the goal of checking if there exists a path from $s$ to $t$ in $\mathbf{G}$. In an optional choice network, we are given a choice set $S\subseteq E\times E$, in addition to the network tuple $\mathbf{G}$. In the $s-t$ reachability problem in choice networks (OCR${}_D$), the goal is to find whether there exists a path from vertex $s$ to vertex $t$, with the caveat that at most one edge from each edge-pair $(x,y)\in S$ is used in the path. OCR${}_D$ finds applications in a number of domains, including routing in wireless networks and sensor placement. We analyze the computational complexities of the OCR${}_D$ problem and its variants from a number of algorithmic perspectives. We show that the problem is NP-complete in directed acyclic graphs with bounded pathwidth. Additionally, we show that its optimization version is NPO PB-complete. Additionally, we show that the problem is fixed-parameter tractable in the cardinality of the choice set $S$. In particular, we show that the problem can be solved in time $O^{\ast }(1.42^{\left|S\right|})$. We also consider weighted versions of the OCR${}_D$ problem and detail their computational complexities; in particular, the optimization version of the $WOC{R}_D$ problem is NPO-complete. While similar results have been obtained for related problems, our results improve on those results by providing stronger results or by providing results for more limited graph types.

在本文中，我们研究了确定的问题$秒-吨$选择网络的可达性。在传统的$秒-吨$可达性问题，我们得到一个加权网络元组$\mathbf{G}=〈V,乙,\mathbf{C},秒,吨〉$，目的是检查是否存在来自$秒$到$吨$在$\mathbf{G}$. 在可选选择网络中，我们有一个选择集$\mathrm{小号}\subseteq 乙\times 乙$, 除了网络元组$\mathbf{G}$. 在里面$秒-吨$选择网络中的可达性问题（OCR${}_{丁}$), 目标是查找是否存在从顶点开始的路径$秒$到顶点$吨$, 需要注意的是每个边对最多有一条边$(X,是)\in \mathrm{小号}$在路径中使用。文字识别${}_{丁}$在许多领域都有应用，包括无线网络中的路由和传感器放置。我们分析了 OCR 的计算复杂度${}_{丁}$从许多算法角度分析问题及其变体。我们表明问题在具有有界路径宽度的有向无环图中是NP 完全问题。此外，我们证明其优化版本是NPO PB-complete。此外，我们表明该问题在选择集的基数中是固定参数可处理的$\mathrm{小号}$. 特别是，我们表明问题可以及时解决${欧}^{＊}(\mathrm{1个}.\mathrm{4个}{\mathrm{2个}}^{\left|\mathrm{小号}\right|})$. 我们还考虑了 OCR 的加权版本${}_{丁}$问题并详细说明它们的计算复杂性；特别是，优化版本的$W欧C{R}_{丁}$问题是NPO-complete。虽然相关问题已经获得了类似的结果，但我们的结果通过提供更强的结果或通过为更有限的图形类型提供结果来改进这些结果。