Graph Connectivity in Log Steps Using Label Propagation
نویسندگان
چکیده
The fastest deterministic algorithms for connected components take logarithmic time and perform superlinear work on a Parallel Random Access Machine (PRAM). These maintain spanning forest by merging compressing trees, which requires pointer-chasing operations that increase memory access latency are limited to shared-memory systems. Many of these PRAM also very complicated implement. Another popular method is “leader-contraction” where the challenge select constant fraction leaders adjacent non-leaders with high probability, but this can require adding more edges than were in original graph. Instead we investigate label propagation because it deterministic, easy implement, does not rely pointer-chasing. Label exchanges representative labels within component using simple graph traversal, inherently difficult complete sublinear number steps. We able overcome problems connectivity. introduce surprisingly framework undirected connectivity easily adaptable many computational models. It achieves convergence independently processors without increasing edge count. employ novel propagating directed alternating direction while performing minimum reduction vertex labels. present new PRAM, Stream, MapReduce. Given simple, [Formula: see text] vertices, edges, our approach takes O(m) each step, only prove path was conjectured Liu Tarjan (2019) steps or possibly Our experiments range graphs suggest convergence. leave proof as an open problem.
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ژورنال
عنوان ژورنال: Parallel Processing Letters
سال: 2021
ISSN: ['0129-6264', '1793-642X']
DOI: https://doi.org/10.1142/s0129626421500213