In this work, we use algebraic methods for studying distance computation and subgraph detection tasks in the congested clique model. Specifically, we adapt parallel matrix multiplication implementations to the congested clique, obtaining an O(n 1−2/ω ) round matrix multiplication algorithm, where ω < 2.3728639 is the exponent of matrix multiplication. In conjunction with known techniques from centralised algorithmics, this gives significant improvements In addition, we present a novel constant-round combinatorial algorithm for detecting 4-cycles.
For APSP, the matrix multiplication algorithms of REF give O(n 1−2/ω ) for the unweighted undirected case.
Algebraic methods in the congested clique
Distributed Computing
Distributed Computing
Computer Science Engineering