Motivated by multi-domain Service Function Chain (SFC) orchestration, we define the Shortest-Longest Path (SLP) problem, prove its hardness, and design an efficient Fully Polynomial Time Approximation Scheme (FPTAS) using the scaling and rounding technique to compute an approximation solution with provable performance guarantee. The SLP problem and its solution algorithm have theoretical significance in multicriteria optimization and also have application potential in QoS routing and multi-domain network resource allocation scenarios.

翻译：受多域服务功能链（SFC）编排的启发，我们定义了最短-最长路径（SLP）问题，证明了其计算困难性，并利用缩放与舍入技术设计了一种高效的完全多项式时间近似方案（FPTAS），以计算具有可证明性能保证的近似解。该SLP问题及其求解算法在多目标优化中具有理论意义，同时在QoS路由与多域网络资源分配场景中具备应用潜力。