On the Power of Some PRAM Models

The focus here is the power of some underexplored CRCW PRAMs, which are strictly more powerful than exclusive write PRAM but strictly less powerful than BSR. We show that some problems can be solved more efficiently in time and/or processor bounds on these models. For example, we show that n linearly-ranged integers can be sorted in O(log n= log log n) time with optimal linear work on Sum CRCW PRAM. We also show that the maximum gap problem can be solved within the same resource bounds on Maximum CRCW PRAM. Though some models can be shown to be more powerful than others, some of them appear to have incomparable powers. Keywords: PRAM; BSR; time and processor bounds; simulation; sorting. Classification Categories: F.1.1, F.1.2, F.2.2 1 Preliminaries The focus of this work is on some underexplored Concurrent Read Concurrent Write (CRCW) Parallel Random Access Machine (PRAM) models. These PRAM models differ only in the way of resolving write conflicts. Some of them can be shown to be s..