The Steiner Shortest Path Tree Problem
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908524930400256 |
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| author | Asher, Omer Dinitz, Yefim Dolev, Shlomi Raviv, Li-on Schieber, Baruch |
| author_facet | Asher, Omer Dinitz, Yefim Dolev, Shlomi Raviv, Li-on Schieber, Baruch |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_06789 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Steiner Shortest Path Tree Problem Asher, Omer Dinitz, Yefim Dolev, Shlomi Raviv, Li-on Schieber, Baruch Data Structures and Algorithms 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. |
| title | The Steiner Shortest Path Tree Problem |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2509.06789 |