Retrieval of scattered information by EREW, CREW, and CRCW PRAMs

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Thek-compaction problem arises whenk out ofn cells in an array are non-empty and the contents of these cells must be moved to the firstk locations in the array. Parallel algorithms fork-compaction have obvious applications in processor allocation and load balancing;k-compaction is also an important subroutine in many recently developed oped parallel algorithms. We show that any EREW PRAM that solves thek-compaction problem requires $$\Omega (\sqrt {\log n} )$$ time, even if the number of processors is arbitrarily large andk=2. On the CREW PRAM, we show that everyn-processor algorithm fork-compaction problem requires Ω(log logn) time, even ifk=2. Finally, we show thatO(logk) time can be achieved on the ROBUST PRAM, a very weak CRCW PRAM model.