An FPTAS for Shortest-Longest Path Problem

TL;DR

This paper introduces an FPTAS for the NP-hard shortest-longest path problem, combining dynamic programming and scaling techniques, with implications for network optimization and resource allocation.

Contribution

It presents the first fully polynomial time approximation scheme for the SLP problem, advancing multicriteria optimization methods.

Findings

Developed an FPTAS with provable guarantees

Proved the NP-hardness of the SLP problem

Applicable to QoS routing and multi-domain networks

Abstract

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 dynamic programming (DP) and scaling and rounding (SR) techniques 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.