-trees this covers one of the more important data structures of the last thirty years -trees are primarily used by relational databases to efficiently implement an operation called join -trees have other properties that are also useful for databases including ordering of rows within tablefast delete capabilityand sequential access goals this introduces some terminology from relational databases to motivate the need for -trees the goes on to introduce the -tree data structure and its implementation by the end of this you should have an understanding of -treestheir advantages over other data structuresand you should be able to demonstrate your understanding by implementing -tree that can be used to efficiently process joins in relational databases relational databases while this is not database text we will cover bit of database terminology to demonstrate the need for -tree and its use in relational database relational database consists of entities and relationships between these entities database schema is collection of entities and their relationships schema is specified by entity relationship diagramoften abbreviated er-diagramor logical data structure [ figure provides an er-diagram for database called the dairy database it is used to formulate rations for dairy cattle to maximize milk production each box in fig represents an entity in the database of particular interest in this text are the feedfeedattributeand feedattribtype entities feedlike corn silage or alfalfais composed of many different nutrients nutrients are things like calciumironphosphorusproteinsugarand so on in the dairy database (cspringer international publishing switzerland lee and hubbarddata structures and algorithms with pythonundergraduate topics in computer sciencedoi -- this copy belongs to 'acha