By Caprara A.

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**Extra info for A 3/4-Approximation Algorithm for Multiple Subset Sum**

**Example text**

As the number of nodes increases, the proportion of the ideal speedup decreases, as communication costs and load imbalances begin to appear. The graph flattens out for larger numbers of nodes, which indicates that the algorithm should have a good efficiency when the number of nodes is large. The two curves in the graph show the trend when all configurations are included and when only configurations with P a power of 2 are included. The difference between these two curves clearly shows the preference for powers of two in the algorithm.

Each grid square is further subdivided into a number of slices, so that the number of elements in a slice does not exceed the number that can be held in one processors memory. 2 for k = 3 and P = 6. Each slice in the figure is labeled with two sets of coordinates. One is its slice number and the other is its (row,column) coordinates. The slice number uniquely defines the slice whereas the (row,column) coordinates are shared between all slices in a grid square. 4 This algorithm was first described in [Tridgell et al.

This figure shows the performance of the algorithm on the 128-node AP1000 as N spans a wide range of values, from values which would be easily dealt with on a workstation, to those at the limit of the AP1000’s memory capacity (2 Gbyte). The elements are 32-bit random integers. The comparison function has been put inline in the code, allowing the function call cost (which is significant on the SPARC) to be avoided. The results give the number of elements that can be sorted per second of real time.

### A 3/4-Approximation Algorithm for Multiple Subset Sum by Caprara A.

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