{"ID":2891485,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.17841","arxiv_id":"2507.17841","title":"Better Bounds for Semi-Streaming Single-Source Shortest Paths","abstract":"In the semi-streaming model, an algorithm must process any $n$-vertex graph by making one or few passes over a stream of its edges, use $O(n \\cdot \\text{polylog }n)$ words of space, and at the end of the last pass, output a solution to the problem at hand. Approximating (single-source) shortest paths on undirected graphs is a longstanding open question in this model. In this work, we make progress on this question from both upper and lower bound fronts: We present a simple randomized algorithm that for any $ε\u003e 0$, with high probability computes $(1+ε)$-approximate shortest paths from a given source vertex in \\[ O\\left(\\frac{1}ε \\cdot n \\log^3 n \\right)~\\text{space} \\quad \\text{and} \\quad O\\left(\\frac{1}ε \\cdot \\left(\\frac{\\log n}{\\log\\log n} \\right) ^2\\right) ~\\text{passes}. \\] The algorithm can also be derandomized and made to work on dynamic streams at a cost of some extra $\\text{poly}(\\log n, 1/ε)$ factors only in the space. Previously, the best known algorithms for this problem required $1/ε\\cdot \\log^{c}(n)$ passes, for an unspecified large constant $c$. We prove that any semi-streaming algorithm that with large constant probability outputs any constant approximation to shortest paths from a given source vertex (even to a single fixed target vertex and only the distance, not necessarily the path) requires \\[ Ω\\left(\\frac{\\log n}{\\log\\log n}\\right) ~\\text{passes}. \\] We emphasize that our lower bound holds for any constant-factor approximation of shortest paths. Previously, only constant-pass lower bounds were known and only for small approximation ratios below two. Our results collectively reduce the gap in the pass complexity of approximating single-source shortest paths in the semi-streaming model from $\\text{polylog } n$ vs $ω(1)$ to only a quadratic gap.","short_abstract":"In the semi-streaming model, an algorithm must process any $n$-vertex graph by making one or few passes over a stream of its edges, use $O(n \\cdot \\text{polylog }n)$ words of space, and at the end of the last pass, output a solution to the problem at hand. Approximating (single-source) shortest paths on undirected grap...","url_abs":"https://arxiv.org/abs/2507.17841","url_pdf":"https://arxiv.org/pdf/2507.17841v2","authors":"[\"Sepehr Assadi\",\"Gary Hoppenworth\",\"Janani Sundaresan\"]","published":"2025-07-23T18:09:51Z","proceeding":"cs.DS","tasks":"[\"cs.DS\",\"cs.CC\"]","methods":"[]","has_code":false}