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<g:link controller="logout"><g:message code="topbar.logout" /></g:link> </g:if> <g:else> <g:link controller="login" action="auth"> <g:message code="topbar.login" /></g:link> </g:else> </nobr> </div>

The knapsack problem should be familiar by now I discussed it with a focus on the fractional version in 7, and in 8 we constructed a pseudopolynomial solution using dynamic programming In this section, I ll have a look at both the knapsack problem itself and a few of its friends Let s start with something seemingly simple,10 the so-called partition problem It s really innocentlooking it s just about equitable distribution In its simplest form, the partition problem asks you to take a list of numbers (integers, say) and partition it into two lists with equal sums Reducing SAT to the partition problem is a bit involved, so I m just going to ask you to trust me on this one (or, rather, see the explanation of Garey and Johnson, for example) Moving from the partition problem to others is easier, though.

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Elapsed time covered by trace file Total wait time SQL*Net round-trips Parse calls Executions Fetch calls Think time

Now just add topbar.logout and topbar.login to the messages bundle:

Because there s seemingly so little complexity involved, using other problems to simulate the partition problem can be quite easy Take the problem of bin packing, for example Here we have a set of items with sizes in the range from 0 to k, and we want to pack them into bins of size k Reducing from the partition problem is quite easy: we just set k to half the sum of the numbers Now if the bin packing problem manages to cram the numbers into two bins, the answer to the partition problem is yes; otherwise, the answer is no This means that the bin packing problem is NP-hard Another well-known problem that is simple to state is the so-called subset sum problem Here you once again have a set of numbers, and you want to find a subset that sums to some given constant, k.

The one significant obstacle that had to be overcome was the reorganization of the LOB segment, since it required downtime. Other than that, the changes were approved quickly. New measurements were taken after the table had been reorganized during a maintenance window. The measurements were taken with instrumentation and SQL trace disabled. Throughput varied between 640 and 682 LOBs per minute. This was reasonably close to the extrapolated value of 645 LOBs per minute. Compared to the original throughput, the speedup was more than tenfold.

You can easily change the text to display whatever you want without modifying the GSP You still have to be careful, though. Depending upon how you modify the text associ. ated with the message code, you may have to adjust the WebTest if it is looking for specific text. In a sophisticated application, you will have to make some decisions about functional testing. You need to ask yourself, Should the functional test be run against a single locale or multiple locales If you decide on multiple locales, you will have to write a more robust functional test and pay particular attention to the usage of verifyText. If you re an experienced web developer, you won t be surprised to find out that using the <g:message> tag also starts you on the path of internationalizing the application. The <g:message> tag is locale-aware; the i18n in the directory name to the messages.property file is a giveaway. By default, the tag uses the browser s locale to determine which message bundle to use. Now that you understand message bundles, you can change the default messages displayed to something user friendly when errors occur.

Once again, finding a reduction is easy enough For example, we can reduce from the partition problem, by (once again) setting k to half the sum of the numbers A version of the subset sum problem locks k to zero the problem is still NP-complete, though (Exercise 11-4) Now, let s look at the actual (integral, nonfractional) knapsack problem Let s deal with the 0-1 version first We can reduce from the partition problem again, if we want, but I think it s easier to reduce from subset sum The knapsack problem can also be formulated as a decision problem, but let s say we re working with the same optimization version we ve seen before: we want to maximize the sum of item values, while keeping the sum of item sizes below our capacity.

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