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arXiv · 2509.06789

The Steiner Shortest Path Tree Problem

Omer Asher·Yefim Dinitz·Shlomi Dolev·Li-on Raviv·Baruch Schieber
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Abstract

We introduce and study a novel problem of computing a shortest path tree with a minimum number of non-terminals. It can be viewed as an (unweighted) Steiner Shortest Path Tree (SSPT) that spans a given set of terminal vertices by shortest paths from a given source while minimizing the number of nonterminal vertices included in the tree. This problem is motivated by applications where shortest-path connections from a source are essential, and where reducing the number of intermediate vertices helps limit cost, complexity, or overhead. We show that the SSPT problem is NP-hard. To approximate it, we introduce and study the shortest path subgraph of a graph. Using it, we show an approximation-preserving reduction of SSPT to the uniform vertex-weighted variant of the Directed Steiner Tree (DST) problem, termed UVDST. Consequently, the algorithm of [Grandoni et al., 2023] approximating DST implies a quasi-polynomial polylog-approximation algorithm for SSPT. We present a polynomial polylog-approximation algorithm for UVDST, and thus for SSPT, for a restricted class of graphs.

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Omer Asher, Yefim Dinitz, Shlomi Dolev, Li-on Raviv, Baruch Schieber. 2025-09-08. The Steiner Shortest Path Tree Problem. https://arxiv.org/abs/2509.06789

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