We study the parameterized complexity of finding shortest s-t-paths with an additional fairness requirement. The task is to compute a shortest path in a vertex-colored graph where each color appears (roughly) equally often in the solution. We provide a complete picture of the parameterized complexity landscape of the problem with respect to structural parameters by showing a tetrachotomy including polynomial kernels, fixed-parameter tractability, XP-time algorithms (and W[1]-hardness), and para-NP-hardness.

翻译：我们研究了在附加公平性约束下寻找最短s-t路径的参数化复杂性。该问题要求在顶点着色图中计算一条最短路径，使得解中每种颜色出现次数（大致）相等。通过展示包含多项式核、固定参数可解性、XP时间算法（及W[1]难解性）和para-NP难解性的四重划分，我们针对结构参数完整刻画了该问题的参数化复杂性全景。