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Retrieval of scattered information by EREW, CREW, and CRCW PRAMs. (English) Zbl 0838.68052
Summary: The $$k$$-compaction problem arises when $$k$$ out of $$n$$ cells in an array are on-empty and the contents of these cells must be moved to the first $$k$$-locations in the array. Parallel algorithms for $$k$$-compaction have obvious applications in processor allocation and load balancing; $$k$$-compaction is also an important subroutine in many recently developed parallel algorithms. We show that any EREW PRAM that solves the $$k$$-compaction problem requires $$\Omega(\sqrt{\log n})$$ time, even if the number of processors is arbitrarily large and $$k= 2$$. On the CREW PRAM, we show that every $$n$$-processor algorithm for $$k$$-compaction problem requires $$\Omega(\log\log n)$$ time, even if $$k= 2$$. Finally, we show that $$O(\log k)$$ time can be achieved on the ROBUST PRAM, a very weak CRCW PRAM model.

##### MSC:
 68W15 Distributed algorithms 68Q25 Analysis of algorithms and problem complexity
##### Keywords:
$$k$$-compaction problem
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##### References:
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