  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.
