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  "PageContent": "<h3>A Programmer Writes… (Brendan's Blog)</h3>I recently posted a series of eight articles on my GitHub Pages blog.[Here is the general introduction to the articles…]The knapsack problem is a problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible.Knapsack problemThe knapsack problem and many other problems in combinatorial optimization require the selection of a subset of items to maximize an objective function subject to constraints. A common approach to solving these problems algorithmically involves recursively generating sequences of items of increasing length in a search for the best subset that meets the constraints.I applied this kind of approach using SQL for a number of problems, starting in January 2013 with A Simple SQL Solution for the Knapsack Problem (SKP-1), and I wrote a summary article, Knapsacks and Networks in SQL, in December 2017 when I put the code onto GitHub, sql_demos – Brendan’s repo for interesting SQL.Here is a series of eight articles that aim to provide a more formal treatment of algorithms for item sequence generation and optimization, together with practical implementations, examples and verification techniques in SQL and PL/SQL.List of ArticlesGitHubOptimization Problems with Items and Categories in OracleTwitterThread with Short Recordings[Here is the conclusion to the articles…]We can list here some of the features and concepts considered in the whole series.Sequence Generation4 types of sequence definedsequence generation explained via recursion……implemented by recursion and by iterationOptimization Problemssequence truncation using simple mathsvalue filtering techniques with approximation and boundingtwo-level iterative refinement methodsSQLrecursive SQLmaterializing subqueries via hints or use of temporary tablescycles and some anomaliesstoring sequences of items in SQL by concatenation, nested tables, and linking tablesindex organised tablespartitioned outer joinssplitting concatenated lists into items via row-generationcombining lists of items into concatenated strings by aggregationpassing bind variables into views via system contextsautomated generation of execution plansPL/SQLPL/SQL with embedded SQL as alternative solution methods to recursive SQL……with sequence generation by both recursion and iteration, with performance comparisonsuse of arrays and temporary tables for intermediate storage, with performance comparisonsmethods for compact storage of sequences of itemsuse of PL/SQL functions in SQL and performance effects of context switchingautomated code timingVerification TechniquesAutomationinstallationrunning the solution methodscode instrumentationunit testingblog internal links hierarchy",
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