• I have seen that natural join is just combination of selection and cartesian product but in various websites its said to be as combination of projection and cartesian product and both are completely d...


I have seen that natural join is just combination of selection and cartesian product but in various websites its said to be as combination of projection and cartesian product and both are completely different so which definition should corresponds to it more exactly?
解决方案
There are many different versions of "relational algebra" that differ even in their notion of "relation". There's no one PRODUCT or NATURAL JOIN.
Some versions of the relational algebra have relation headings that are lists of attribute names. PRODUCT outputs an attribute for every input list element. If there's a NATURAL JOIN then its result will be like first doing PRODUCT, then RESTRICTing/SELECTing on equality of pairs of same-named attributes, then PROJECTing out one attribute of each pair. They give the same result when there are no shared attribute names. PRODUCT works for any two inputs but NATURAL JOIN might be undefined when an input has duplicate attribute names.
Some versions of the relational algebra have relation headings that are sets of attribute names. (Elements are unordered & unique.) The result of NATURAL JOIN has a heading that is the union of the input headings. (Tuples have one copy each of the attribute names common to both inputs & one copy each of the attribute names unique to one input.) It returns all tuples with that heading that can be made by combining a tuple from each input table. That is regardless of how many common attribute names there are, including zero. PRODUCT is defined only when the inputs share no attribute names but otherwise acts like NATURAL JOIN. PRODUCT's role is to confirm that you expect that there are no shared attribute names. When all the column names are common, that is a kind of INTERSECTION.
All this is regardless of PKs, UNIQUE, FKs & other constraints.

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• I am studying for exams and am failing to find a solid criteria by which I can determine if the Cartesian Product x is to be used or if Natural Join |X| is to be used.I had come up with a rough guide ...


I am studying for exams and am failing to find a solid criteria by which I can determine if the Cartesian Product x is to be used or if Natural Join |X| is to be used.
I had come up with a rough guide that:
"If you need to project an attribute that has the same name as an attribute in the table to be joined you must use x and state the table names to be projected: tableA.colname1 = tableB.colname1"
This however doesn't follow some of the solutions in my notes and my lecturer seems to use x with the above convention or |x| interchangeably.
Does anyone have a rule that can be followed to define use of one over the other?
Take for example this schema (only schema related to the question quoted for brevity):
takes(ID, course_id, sec_id, semester, year, grade)
student(ID, name, dept_name, tot_cred)
Q) Find the name of all students who took courses that were taught in either Spring 2011 or Autumn 2011.
π name(σ semester="Spring" ^ year=2011(takes ⋈ student)) ∪ π name(σ semester="Autumn" ^ year=2011(takes ⋈ student))
π name(σ semester="Spring" ^ year=2011 ^ takes.ID=student.ID(takes x student)) ∪ π name(σ semester="Autumn" ^ year=2011 ^ takes.ID=student.ID(takes x student))
Can anyone provide a reason as to why?
In my mind the Natural Join would take care of the takes.ID=student.ID?
解决方案
A natural join, as I understand it, is a projected, filtered Cartesian product:
You take the Cartesian product, then
select it, so that the values in columns of the same name have the same value, and
project it, so that all columns have distinct names.
Under this assumption, your answer is isomorphic to the actual answer.
To see this, you might want to expand the natural join to the above sequence of operators, and float them around using the laws of relational algebra. You'll see that the projection disappears due to the projection to name, and the selection criterion is fused with the selection above. You'll end up with exactly the same tree as the actual answer, even though you never changed the meaning of your own answer!
I can think of one reason why your lecturer uses these concepts interchangeably: your lecturer wants you to understand that these concepts can be used interchangeably, because "the natural join is just a shortcut" (though that's debatable).

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• 关系代数中连接是一个重要而且容易混乱的知识点，我通过查阅很多资料总结了与连接有关的知识点，并发现了他们之间的关系。本文通过理论知识先了解连接相关的重要名词意思，然后通过画图来理解画连接的思路以及他们...

摘要：微信搜索【三桥君】 前言：关系代数中的连接是一个重要而且容易混乱的知识点，我通过查阅很多资料总结了与连接有关的知识点，并发现了他们之间的关系。本文通过理论知识先了解连接相关的重要名词意思，然后通过画图来理解画连接的思路以及他们之间的关系。

理论知识
定义：
一、笛卡儿积  二、θ连接  （一）等值连接  （二）非等值连接 θ不为“=”的连接运算称为非等值连接。
三、自然连接  五、外连接  （一）左外连接（Left outer join/ left join） 如果只把左边关系R要舍弃的元组在自然连接的基础上保留就叫左外连接。 （二）右外连接（rightouter join/ right join） 如果只把右边关系S中要舍弃的元组在自然连接的基础上保留叫右外连接。 （三）全外连接（fullouter join/ full join） 左表和右表都不做限制，所有的记录都显示，两表不足的地方用null 填充。
画图
题目  一、笛卡儿积  二、θ连接 （一）等值连接  （二）非等值连接  三、自然连接  五、外连接

文章整理不易，如有帮助请点赞关注支持，谢谢！微信搜索【三桥君】，回复【关注】有我准备的一份资源大礼包。后续持续更新~~~

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• MapReduce关系代数运算——自然连接 关系沿用之前的R。 创建两个文件 表1 student id name sex age 1 Amy female 18 2 Tom male 19 3 Sam male 21 4 John male ...
MapReduce关系代数运算——自然连接
关系沿用之前的R。
创建两个文件

表1 student

idnamesexage1Amyfemale182Tommale193Sammale214Johnmale195Lilyfemale216Rosefemale20

MapReduce程序设计
NaturalJoinMap
import org.apache.hadoop.io.IntWritable;

public class NaturalJoinMap extends Mapper<LongWritable, Text, IntWritable, Text> {

private String fileName = "";
private Text val = new Text();
private IntWritable stuKey = new IntWritable();

protected void setup(Context context) throws java.io.IOException, InterruptedException {
FileSplit fileSplit = (FileSplit) context.getInputSplit();
fileName = fileSplit.getPath().getName();
};

protected void map(LongWritable key, Text value, Context context) throws java.io.IOException, InterruptedException {
String[] arr = value.toString().split(" ");
stuKey.set(Integer.parseInt(arr[0]));
val.set(fileName + " " + value.toString());
context.write(stuKey, val);
};

}

NaturalJoinReduce
import java.util.ArrayList;
import java.util.List;

public class NaturalJoinReduce extends Reducer<IntWritable, Text, Text, NullWritable> {

private Text student = new Text();
private Text value = new Text();

protected void reduce(IntWritable key, Iterable<Text> values, Context context) throws java.io.IOException, InterruptedException {
List<String> grades = new ArrayList<String>();
for (Text val : values) {
if (val.toString().contains("student")) {
student.set(studentStr(val.toString()));
} else {
}
}
context.write(value, NullWritable.get());
}
};

private String studentStr(String line) {
String[] arr = line.split(" ");
StringBuilder str = new StringBuilder();
for (int i = 1; i < arr.length; i++) {
str.append(arr[i] + " ");
}
return str.toString();
}

private String gradeStr(String line) {
String[] arr = line.split(" ");
StringBuilder str = new StringBuilder();
for (int i = 2; i < arr.length; i++) {
str.append(arr[i] + " ");
}
return str.toString();
}

}

NaturalJoin
import java.io.IOException;

public class NaturalJoin {

public static void main(String[] args) throws IOException, ClassNotFoundException, InterruptedException {
if (args == null || args.length != 2) {
throw new RuntimeException("请输入输入路径、输出路径");
}
Configuration conf = new Configuration();
Job job = Job.getInstance(conf);
job.setJobName("NaturalJoin");
job.setJarByClass(NaturalJoin.class);

job.setMapperClass(NaturalJoinMap.class);
job.setMapOutputKeyClass(IntWritable.class);
job.setMapOutputValueClass(Text.class);

job.setReducerClass(NaturalJoinReduce.class);
job.setOutputKeyClass(IntWritable.class);
job.setOutputValueClass(NullWritable.class);

FileOutputFormat.setOutputPath(job, new Path(args[1]));
System.exit(job.waitForCompletion(true) ? 0 : 1);
}

}


运行
像之前的WordCount一样将代码打包出来，生成NaturalJoin .jar文件：
hadoop jar NaturalJoin .jar /input /output relationB

输出结果：  欢迎查看我的博客：Welcome To Ryan’s Home
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• ## 关系代数运算之连接运算

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