The Taub Faculty of Computer Science Events and Talks

The cost of accessing shared objects that are stored in remote memory, while neglecting accesses to shared objects that are cached in the local memory, is evaluated by the number of remote memory references (RMRs) in an execution. two flavours of this measure- cache-coherent (CC) and distributed shared memory (DSM)-model two popular shared-memory architectures. The number of RMRs, however, does not take into account the granularity of memory accesses, namely, the fact that accesses to the shared memory are performed in blocks. This thesis proposes a new measure, called block RMRs, counting the number of remote memory references while taking into account the fact that shared objects can be grouped into blocks. On the one hand, this measure reflects the fact that the RMR paid for bringing a shared object to the local memory might save another RMR for bringing another object placed at the same block. On the other hand, this measure accounts for false sharing: the fact an RMR may be paid when accessing an object due to a concurrent access to another object in the same block. This paper proves that in the CC model finding an optimal placement, i.e., grouping of objects into blocks, is NP-hard when a block can store three objects or more; the result holds even if the sequence of accesses is known in advance. In the DSM model, the answer depends on the cost of invalidating data throughout the system. If cache coherence is supported (i.e., some mechanism exists to inform processes that the data in their local memory is no longer valid), and if the cost of invalidation is negligible compared to the cost of an RMR, then finding an optimal solution is NP-hard. If invalidation is not negligible, an optimal layout can be approximated within an additive factor (depending on the number of processes), if the sequence of accesses is known in advance. In both the CC and the DSM models, finding an optimal placement is NP-hard when objects have different sizes, even for a single process.