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A nearly optimal distributed algorithm for computing the weighted girth

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Abstract

Computing the weighted girth, which is the sum of weights of edges in the minimum weight cycle, is an important problem in network analysis. The problem for distributively computing girth in unweighted graphs has garnered lots of attention, but there are few studies in weighted graphs. In this paper, we propose a distributed randomized algorithm for computing the weighted girth in weighted graphs with integral edge weights in the range [1, nc], where n is the number of vertices and c is a constant. The algorithm is devised under the standard synchronous \({\cal C}{\cal O}{\cal N}{\cal G}{\cal E}{\cal S}{\cal T}\) model, which limits each vertex can only transfer O(log n) bits information along each incident edge in a round. The upper bound of the algorithm is O(n log2n) rounds. We also prove the lower bound for computing the weighted girth is Ω(D + n/ log n) where D is the hop diameter of the weighted graph. This means our distributed algorithm is optimal within a factor of O(log3n).

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Acknowledgements

This work was supported in part by National Key Research and Development Program of China (Grant No. 2018YFB1003203), National Natural Science Foundation of China (Grants No. 61972447), and Fundamental Research Funds for the Central Universities (Grant No. 2019kfyXKJC021). We thank the anonymous reviewers for the helpful comments to improve the presentation of this paper.

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Authors and Affiliations

  1. National Engineering Research Center for Big Data Technology and System/Services Computing Technology and System Lab/Cluster and Grid Computing Lab, School of Computer Science and Technology, Huazhong University of Science and Technology, Wuhan, 430074, China

    Qiang-Sheng Hua, Lixiang Qian, Xuanhua Shi & Hai Jin

  2. School of Computer Science and Technology, Shandong University, Qingdao, 266237, China

    Dongxiao Yu

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  1. Qiang-Sheng Hua
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  2. Lixiang Qian
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  3. Dongxiao Yu
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  4. Xuanhua Shi
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  5. Hai Jin
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Correspondence to Qiang-Sheng Hua.

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Hua, QS., Qian, L., Yu, D. et al. A nearly optimal distributed algorithm for computing the weighted girth. Sci. China Inf. Sci. 64, 212101 (2021). https://doi.org/10.1007/s11432-020-2931-x

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