Retrieval of scattered information by EREW, CREW and CRCW PRAMs

The k-compaction problem arises when k out of n cells in an array are non-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\Gamma p 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\Gammaqui 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