Polynomial-time algorithms for wider graph classes

Develop polynomial-time algorithms for the restricted inverse optimal value problem on shortest paths under the weighted l∞ norm for graph classes wider than trees, such as series-parallel graphs or bounded-treewidth networks.

Background

The paper establishes exact O(n log n)-time algorithms for the restricted inverse optimal value problem on shortest root–leaf paths under the weighted l∞ norm when the underlying network is a tree. The authors explicitly identify extending these results beyond trees as unresolved, mentioning series-parallel graphs and bounded-treewidth networks as candidate graph classes that may retain polynomial-time solvability.