HBJ model

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In computer science, the Helman-Bader-JaJa model ^[1] is a concise message-passing model of parallel computing defined with the following parameters:

• ${\displaystyle p}$ is number of processors.
• ${\displaystyle n}$ is the problem size.
• ${\displaystyle m}$ is number of machine words in a packet sent over the network.
• ${\displaystyle \tau }$ is the latency, or time at which a processor takes to initiate a communication on a network.
• ${\displaystyle \sigma }$ is the bandwidth, or time per machine word at which a processor can inject or receive ${\displaystyle m}$ machine words from the network.
• ${\displaystyle T_{comp}}$ is the largest computation time expended on a processor.
• ${\displaystyle T_{comm}}$ is the time spent in communication on the network.

This model assumes that for any subset of ${\displaystyle q}$ processors, a block permutation among the ${\displaystyle q}$ processors takes ${\displaystyle (\tau +\sigma m)}$ time, where ${\displaystyle m}$ is the size of the largest block.

1. ^ David R., Helman; David A., Bader; JaJa, Joseph (1998). "A Randomized Parallel Sorting Algorithm with an Experimental Study" (PDF). Journal of Parallel and Distributed Computing. 52: 1–23. doi:10.1006/jpdc.1998.1462. hdl:1903/835. Archived from the original (PDF) on 19 November 2012. Retrieved 26 October 2012.
2. ^ Bader, David A.; Jaja, Joseph (1996). "Practical parallel algorithms for dynamic data redistribution, median finding, and selection". Proceedings of the 10th IEEE International Parallel Processing Symposium: 292–301.

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