A simple Path-based LP Relaxation for Directed Steiner Tree
Data Structures and Algorithms
2026-03-04 v1
Abstract
We study the Directed Steiner Tree (DST) problem in layered graphs through a simple path-based linear programming relaxation. This relaxation achieves an integrality gap of O(l log k), where k is the number of terminals and l is the number of layers, which matches the best known bounds for DST previously obtained via lift-and-project hierarchies. Our formulation bypasses hierarchy machinery, offering a more transparent route to the state-of-the-art bound, and it can be exploited to provide an alternative simpler proof that O(l) rounds of the Sherali-Adams hierarchy suffice for reducing the integrality gap on layered instances of DST.
Keywords
Cite
@article{arxiv.2603.02825,
title = {A simple Path-based LP Relaxation for Directed Steiner Tree},
author = {Kanstantsin Pashkovich and Marta Pozzi and Laura Sanità},
journal= {arXiv preprint arXiv:2603.02825},
year = {2026}
}