Consider an undirected network with traversal times on its edges and a set of commodities with connection requests from sources to destinations and release dates. The non-stop disjoint trajectories problem is to find trajectories that fulfill all requests, such that the commodities never meet. In this extension to the -complete disjoint paths problem, trajectories must satisfy a non-stop condition, which disallows waiting at vertices or along arcs. This problem variant appears, for example, when disjoint aircraft trajectories shall be determined or in bufferless packet routing. We study the border of tractability for feasibility and optimization problems on three graph classes that are frequently used where space and time are discretized simultaneously: the path, the grid, and the mesh. We show that if all commodities have a common release date, feasibility can be decided in polynomial time on paths. For the unbounded mesh and unit-costs, we show how to construct optimal trajectories. In contrast, if commodities have individual release intervals and turns are forbidden, then even feasibility is -complete for the path. For the mesh and arbitrary edge costs, with individual release dates and turning abilities of commodities restricted to at most 90°, we show that optimization and approximation are not fixed-parameter tractable.

中文翻译：

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不间断不相交轨迹问题

考虑一个无向网络，其边缘有遍历时间，以及一组具有从源到目的地的连接请求和发布日期的商品。不间断不相交轨迹问题是找到满足所有要求的轨迹，使得商品永远不会相遇。在完全不相交路径问题的扩展中，轨迹必须满足不间断条件，该条件不允许在顶点或沿弧线等待。例如，当应确定不相交的飞机轨迹或在无缓冲数据包路由中时，就会出现此问题变体。我们研究了空间和时间同时离散化时经常使用的三种图类的可行性和优化问题的易处理性边界：路径、网格和网格。我们证明，如果所有商品都有一个共同的发布日期，则可以在路径上的多项式时间内确定可行性。对于无界网格和单位成本，我们展示了如何构建最佳轨迹。相反，如果商品有单独的释放间隔并且禁止转弯，那么该路径的可行性也是完整的。对于网格和任意边缘成本，单个发布日期和商品的转动能力最多限制为 90°，我们表明优化和近似不是固定参数可处理的。