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arXiv · 2603.02825

A simple Path-based LP Relaxation for Directed Steiner Tree

Kanstantsin Pashkovich·Marta Pozzi·Laura Sanità
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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.

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Kanstantsin Pashkovich, Marta Pozzi, Laura Sanità. 2026-03-03. A simple Path-based LP Relaxation for Directed Steiner Tree. https://arxiv.org/abs/2603.02825

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