Abstract
When executing processes on parallel computer systems a major bottle-neck is interprocessor communication. One way to address this problem is to minimize the communication between processes that are mapped to different processors. This translates to the k-partitioning problem of the corresponding process graph, where k is the number of processors. The classical spectral lower bound of (|V|/2k)\sumk i=1λ i for the k-section width of a graph is well known. We show new relations between the structure and the eigenvalues of a graph and present a new method to get tighter lower bounds on the k-section width. This method makes use of the level structure defined by the k-section. We define a global expansion property and prove that for graphs with the same k-section width the spectral lower bound increases with this global expansion. We also present examples of graphs for which our new bounds are tight up to a constant factor.
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Elsässer, R., Lücking, T. & Monien, B. On Spectral Bounds for the k-Partitioning of Graphs. Theory Comput Systems 36, 461–478 (2003). https://doi.org/10.1007/s00224-003-1083-9
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DOI: https://doi.org/10.1007/s00224-003-1083-9