Breaking the Sorting Barrier for Directed Single-Source Shortest Paths

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Conflicts of Interest

Identified Weaknesses

Rating Explanation

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Paper Summary

Paperzilla title

Zippier Shortest Paths on One-Way Streets (But Only If Sparse)

This paper introduces a deterministic algorithm for the single-source shortest path (SSSP) problem on directed graphs with non-negative edge weights. The algorithm achieves a time complexity of O(m log^(2/3) n), improving upon Dijkstra's algorithm for sparse graphs. This is the first deterministic algorithm to break the O(m + n log n) time bound in this setting.

Possible Conflicts of Interest

None identified

Identified Weaknesses

Limited to sparse graphs

The algorithm's improvement is primarily for "sparse" graphs with fewer connections, and may not be as significant for dense, highly interconnected graphs.

Lack of empirical evaluation

While the paper provides theoretical guarantees, practical implementations and comparisons with existing algorithms are needed to assess real-world performance.

Constant degree assumption

The algorithm's dependence on constant in- and out-degrees might require transforming the original graph, which can introduce overhead.

Rating Explanation

The paper offers a significant theoretical advancement in shortest path algorithms by breaking the sorting barrier for directed sparse graphs. While lacking empirical validation, the theoretical contribution warrants a strong rating. The limitations to sparse graphs and reliance on constant degrees are noted but do not diminish the core contribution.

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