One Step Closer towards a Realistic Model for Parallel Computation

We present a new model of parallel computation|the LogGP model|and use it to analyze a number of algorithms, most notably, the single node scatter (one-to-all personalized broadcast). The LogGP model is an extension of the LogP model for parallel computation CKP + 93] which abstracts the communication of xed-sized short messages through the use of four parameters: the communication latency (L), overhead (o), bandwidth (g), and the number of processors (P). As evidenced by experimental data, the LogP model can accurately predict communication performance when only short messages are sent (as on the CM-5) CKP + 93, CDMS93]. However, many existing parallel machines have special support for long messages and achieve a much higher bandwidth for long messages compared to short messages (e.g., IBM SP-2, Paragon, Meiko CS-2, Ncube/2). We extend the basic LogP model with a linear model for long messages. This combination, which we call the LogGP model of parallel computation, has one additional parameter , G, which captures the bandwidth obtained for long messages. Experimental data collected on the Meiko CS-2 shows that this simple extension of the LogP model can quite accurately predict communication performance for both short and long messages. This paper discusses algorithm design and analysis under the new model, examining the all-to-all remap, FFT, and radix sort. We also examine, in more detail, the single node scatter problem. We derive solutions for this problem and prove their optimality under the LogGP model. These solutions are qualitatively diierent from those obtained under the simpler LogP model, reeecting the importance of capturing long messages in a model.