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Emerging memory technologies have a significant gap between the cost, both intime and in energy, of writing to memory versus reading from memory. In thispaper we present models and algorithms that account for this difference, with afocus on write-efficient sorting algorithms. First, we consider the PRAM modelwith asymmetric write cost, and show that sorting can be performed in$O\left(n\right)$ writes, $O\left(n \log n\right)$ reads, and logarithmic depth(parallel time). Next, we consider a variant of the External Memory (EM) modelthat charges $\omega > 1$ for writing a block of size $B$ to the secondarymemory, and present variants of three EM sorting algorithms (multi-waymergesort, sample sort, and heapsort using buffer trees) that asymptoticallyreduce the number of writes over the original algorithms, and perform roughly$\omega$ block reads for every block write. Finally, we define a variant of theIdeal-Cache model with asymmetric write costs, and present write-efficient,cache-oblivious parallel algorithms for sorting, FFTs, and matrixmultiplication. Adapting prior bounds for work-stealing andparallel-depth-first schedulers to the asymmetric setting, these yield parallelcache complexity bounds for machines with private caches or with a sharedcache, respectively.

Sorting with Asymmetric Read and Write Costs