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- W4383988178 abstract "In undirected graphs with real non-negative weights, we give a new randomized algorithm for the single-source shortest path (SSSP) problem with running time $O(msqrt{log n cdot loglog n})$ in the comparison-addition model. This is the first algorithm to break the $O(m+nlog n)$ time bound for real-weighted sparse graphs by Dijkstra's algorithm with Fibonacci heaps. Previous undirected non-negative SSSP algorithms give time bound of $O(malpha(m,n)+min{nlog n, nloglog r})$ in comparison-addition model, where $alpha$ is the inverse-Ackermann function and $r$ is the ratio of the maximum-to-minimum edge weight [Pettie & Ramachandran 2005], and linear time for integer edge weights in RAM model [Thorup 1999]. Note that there is a proposed complexity lower bound of $Omega(m+min{nlog n, nloglog r})$ for hierarchy-based algorithms for undirected real-weighted SSSP [Pettie & Ramachandran 2005], but our algorithm does not obey the properties required for that lower bound. As a non-hierarchy-based approach, our algorithm shows great advantage with much simpler structure, and is much easier to implement." @default.
- W4383988178 created "2023-07-12" @default.
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- W4383988178 date "2023-07-09" @default.
- W4383988178 modified "2023-10-06" @default.
- W4383988178 title "A Randomized Algorithm for Single-Source Shortest Path on Undirected Real-Weighted Graphs" @default.
- W4383988178 doi "https://doi.org/10.48550/arxiv.2307.04139" @default.
- W4383988178 hasPublicationYear "2023" @default.
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