Approximate compaction and padded-sorting on exclusive write PRAMs

Padded-sorting is a task of placing input items in an array in a nondecreasing order, but with free space between consecutive elements allowed. For many applications, padded-sorting is as useful as sorting. Approximate compaction and compression are closely related problems. It is known that the time complexity of padded-sorting on randomized CRCW PRAMs is considerably lower than the time complexity of sorting. We analyze the time complexity of these problems on CREW and EREW PRAMs (deterministic and randomized) and get tight lower and upper bounds depending on the size of free space. We extend our lower bounds to approximate compaction and compression. Some of the algorithms presented are very rare examples of randomized EREW PRAMs that are much faster than their deterministic counterparts