Lower bounds for parallel computation
This thesis explores methods of proving lower bounds on the time to solve problems in theoretical models of parallel computation. The focus is on the Concurrent-Read Concurrent-Write Parallel Random Access Machine (CRCW PRAM), a highly parallel model in which several synchronous processors communicate by means of shared memory cells that all processors can access. Any number of processors may simultaneously access the same memory cell for the purpose of reading or writing a value. The input to such a machine is placed in shared memory, or distributed among the local memories of the processors. When the number of processors is fixed, the power of the CRCW PRAM depends on two resources: the number of shared memory cells, and the method of write-conflict resolution. The latter is used to decide the outcome in the case that several processors attempt to simultaneously write different values into the same shared-memory cell. The results described here show lower bounds which separate the power of machines with different write-conflict resolution methods in the case when the size of shared memory is kept small relative to the number of processors, and when the size of shared memory is unbounded. Many of the results are extended to the case where processors are allowed the power of making probabilistic choices. Algorithms that allow a weaker machine to simulate any computation of a more powerful machine are given, and proved optimal.
- Research Organization:
- California Univ., Berkeley (USA)
- OSTI ID:
- 5263000
- Country of Publication:
- United States
- Language:
- English
Similar Records
A lower bound for the QRQW PRAM
Recursive star-tree parallel data structure. Technical report