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communication between them. Let s say one of the processors is a GPU and that the processes have different running times on the two processors. Some fit the CPU better, while some should be run on the GPU. However, there might be cases where one fits on the CPU and one on the GPU, but where the two communicate extensively with each other. In that case, we might want to put them on the same processor, just to reduce the communication costs. How would we solve this We could set up an undirected flow network with the CPU as the source and the GPU as the sink, for example. Each process would have an edge to both source and sink, with a capacity equal to the time it would take to run on that processor. We also add edges between processes that communicate, with capacities representing the communication overhead (in extra computation time) of having them on separate processors. The minimum cut would then distribute the processes on the two processors in such a way that the total cost is as small as possible a nontrivial task if we couldn t reduce to the min-cut problem. In general, you can think of the whole flow network formalism as a special kind of algorithmic machine, and you can use it to solve other problems by reduction. The task becomes constructing some form of flow network where a maximum flow or minimum cut represents a solution to your original problem.

Listing 5-2. The Main Layout (main.gsp)

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There are a couple of examples of duality in this chapter: maximum bipartite matchings are the dual of minimum bipartite vertex covers, and maximum flows are the dual of minimum cuts. There are several similar cases as well, such as the maximum tension problem, which is the dual of the shortest path problem. In general duality involves two optimization problems, the primal and the dual, where both have the same optimization cost, and solving one will solve the other. More specifically, for a maximization problem A and a minimization problem B, we have weak duality if the optimal solution for A is less than or equal to the optimal solution for B. If they are equal (as for the max-flow min-cut case), we have strong duality. If you want to know more about duality (including some rather advanced material), take a look at Duality in Optimization and Variational Inequalities, by Go and Yang.

All the statistics calculated and their sources are summarized in Table 27-1.

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Before leaving the topic of flow, let s take a look at an important and rather obvious extension; let s find the cheapest maximum flow. That is, we still want to find the maximum flow, but if there are more than one way to achieve the same flow magnitude, we want the cheapest one. We formalize this by adding costs to the edges and define the total cost as the sum of w(e) f (e) over all edges e, where w and f are the cost and flow functions, respectively. That is, the cost is per unit of flow over a given edge. An immediate application of this is an extension of the bipartite matching problem. We can keep using the zero-one flow formulation but add costs to each of the edges. We then have a solution to the min-cost bipartite matching (or assignment) problem, hinted at in the introduction: by finding a maximum flow, we know we have a maximum matching, and by minimizing the cost, we get the matching we re looking for. This problem is often referred to simply as min-cost flow. That means that rather than looking for the cheapest maximum flow, we re simply looking for the cheapest flow of a given magnitude. For example, the problem might be give me a flow of size k, if such a flow exists, and make sure you

cr, cu, and p in PARSE, EXEC, and FETCH entries cr in PARSE, EXEC, and FETCH entries parameter mis in PARSE entries cu in PARSE, EXEC, and FETCH entries WAIT entries with nam='enqueue'or 'enq: enqueue_details', where enqueue_details contains the name of an enqueue and a short description (e.g., nam='enq: TX contention') WAIT entries with nam='latch free'or 'latch: latch_details , where latch_details contains the name of a latch and a short description (e.g., nam='latch: cache buffers chains') p in PARSE, EXEC, and FETCH entries r in PARSE, EXEC, and FETCH entries p3 (Oracle9i and prior releases) or blocks (Oracle10g) of the wait events db file sequential read and db file scattered read R and XCTEND rlbk=0, rd only=0

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This section is a bit hard and is not essential in order to understand the rest of the book. Feel free to skim it or even skip it entirely. You might want to read the first couple of paragraphs, though, to get a feel for the problem.

The small trace file used in the previous case study did not contain any waits for enqueues or latches. Hence the latch wait and enqueue wait sections in the preceding code example are empty. Following is an excerpt of an ESQLTRCPROF report, which resulted from tracing database sessions that were concurrently enqueuing messages into an Advanced Queuing queue table. The excerpt illustrates that the sessions were contending for both latches and enqueues. Latch wait breakdown -----------------------row cache objects library cache pin commit callback allocation cache buffers chains dml lock allocation library cache enqueue hash chains

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