Approximate Parallel Scheduling Part Ii Applications to Optimal Parallel Graph

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Approximate Parallel Scheduling Part Ii Applications to Optimal Parallel Graph
Richard Cole
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Each copy has a successor in its own list. In parallel, we make the successor of each copy of each causing edge the successor of the other copy of the same causing edge. An argument similar to [AV-84] shows that this indeed gives a single circular list for each new supervertex.
The number of operations required is proportional to the number of causing edges (or rather the number of edges used in Step 2), which is 0(m/d). The time is 0(1). This is- charged to a miscellaneous budget. Over the who
...le algorithm this is 0(m) operations and C>(log n) time.
It is convenient to place the dummy clusters introduced in this phase into the array of clusters. To do this we need to assign a serial number to each such dummy cluster; this is readily computed by means of a prefix sum computation with respect to the array of edges used in Step 2. Per phase this takes 0(log nAog^'^^n) time and 0(m/d) operations. This is charged to a miscellaneous budget. Over the whole algorithm this is 0{m) operations and 0(log n) time.


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