Problem
Research questions and friction points this paper is trying to address.
directed hopsets
shortcut sets
distance preservers
graph algorithms
Faster Directed Hopsets, Distance Preservers, and Deterministic Shortcut Sets
🤖 AI Summary
This study addresses the inefficiency in constructing distance structures for directed graphs by proposing faster algorithms for directed (1+ε)-hopsets, deterministic shortcut sets, and source-wise distance preservers. Methodologically, this work presents the first efficient algorithms that match the latest theoretical bounds, extending them to general graphs via DAG projection techniques while optimizing the computational pipeline through structured hopset analysis and accelerated reduction strategies. By significantly improving the construction speed of directed graph distance structures and achieving state-of-the-art trade-offs between size and hop count, this project provides novel theoretical and practical foundations for shortest path problems in directed graphs.
📝 Abstract
While there have been many recent advances in getting better tradeoffs for directed distance structures such as hopsets, shortcut sets and distance preservers, most known algorithms are inefficient. In this work we provide three results:
- Faster algorithms for directed $(1+ε)$-hopsets, matching the state-of-the-art size/hopbound trade-offs of Bernstein & Wein [SODA23]. Our algorithm is first designed for DAGs and then extended to general graphs (up to $n^{o(1)}$ factors) using the recent DAG projection result of Haeupler, Jiang, and Saranurak [STOC26].
- Faster \textit{deterministic} algorithms for constructing shortcut sets, matching the state-of-the-art size/hopbound tradeoffs of Kogan & Parter [SODA22A].
- Using our improved directed hopset construction, we get significantly faster algorithms for computing source-wise distance preservers. This algorithm is based on speeding-up reductions of Kogan & Parter [SODA22B] by using certain structural properties of our hopsets.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Directed Hopsets
Shortcut Sets
Distance Preservers
Deterministic Algorithms
DAG Projection
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