A nearly optimal distributed algorithm for computing the weighted girth

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...

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Veröffentlicht in:Science China. Information sciences Jg. 64; H. 11; S. 212101
Hauptverfasser: Hua, Qiang-Sheng, Qian, Lixiang, Yu, Dongxiao, Shi, Xuanhua, Jin, Hai
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Beijing Science China Press 01.11.2021
Springer Nature B.V
Schlagworte:
Algorithms
Apexes
Computation
Computer Science
Graphs
Information Systems and Communication Service
Lower bounds
Minimum weight
Network analysis
Research Paper
Upper bounds
weighted girth
model
communication complexity
round complexity
distributed algorithms
ISSN:1674-733X, 1869-1919
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Zusammenfassung: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, n c ], where n is the number of vertices and c is a constant. The algorithm is devised under the standard synchronous C O N G ℰ S 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 log 2 n ) 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 (log 3 n ).
Bibliographie:ObjectType-Article-1
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ISSN:1674-733X
1869-1919
DOI:10.1007/s11432-020-2931-x