Abstract.A crucial problem that needs to be solved is the allocation of memory to processors in a pipeline. Ideally, the processor memories should be totally separate (i.e., one-port memories) in order to minimize contention; however, this minimizes memory sharing. Idealized sharing occurs by using a single shared memory for all processors but this maximizes contention. Instead, in this paper we show that perfect memory sharing of shared memory can be achieved with a collection of two-port memories, as long as the number of processors is less than the number of memories. We show that the problem of allocation is NP-complete in general, but has a fast approximation algorithm that comes within a factor of 3 2 asymptotically. The proof utilizes a new bin packing model, which is interesting in its own right. Further, for important special cases that arise in practice a more sophisticated modification of this approximation algorithm is in fact optimal. We also discuss the online memory allocation problem and present fast online algorithms that provide good memory utilization while allowing fast updates.

In the well-studied Majority problem, we are given a set of n balls colored with two or more colors, and the goal is to use the minimum number of color comparisons to find a ball of the majority color (i.e., a color that occurs for more than n/2 times). The Plurality problem has exactly the same setting while the goal is to find a ball of the dominant color (i.e., a color that occurs most often). Previous literature regarding this topic dealt mainly with adaptive strategies, whereas in this paper we focus more on the oblivious (i.e., non-adaptive) strategies. Given that our strategies are oblivious, we establish a linear upper bound for the Majority problem with arbitrarily many different colors assuming a majority label exists. We then show that the Plurality problem is significantly more difficult by establishing quadratic lower and upper bounds. In the end we also discuss some generalized upper bounds for adaptive strategies in the k-color Plurality problem.

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