使用SQL的图形中的最长路径

Question

I've a graph which is saved as two tables with names Edge and Node as follows in SQL:

Node table:
Id Name
10 A
11 B
12 C

Edge Table:
From To Weight
10 11 0.3
10 14 0.2
10 12 0.5
11 12 0.6
12 10 0.8

For example one possible solution for path from node 10 to node 12 is as follows:

From    To  Weight  Path
10  12  0.9 10,11,12

Now, I want to find out the longest path between nodes of the graph (for any possible path).

I've changed dijkstra with negative edges and it looped and doesn't return any result.

Is there any procedure or algorithm to find out the desired result?

Answer 1

Recently I had a similar issue and tried to find the longest path using SQL recursive CTE query . Please refer to given article.

I tried to modify the above solution for your problem, and get a list of all possible paths as seen in following output screen

If this is the result you want to achive, I can continue describing my solution on SQL Server

The referred SQL query calculates the longest path for given two nodes. So first of all we need to define all possible starting and destination nodes

Below query lists the combination of all possible sets

select Nodes_From.Id as [From], Nodes_To.Id as [To]
from LongestPath_Nodes as Nodes_From
inner join LongestPath_Nodes as Nodes_To
    on Nodes_From.Id <> Nodes_To.Id

Please note that this excludes "14" for example since it is not in the nodes table (so there is a consistency problem here actually in given test data)

So by creating a SQL cursor , I can loop through each node set (from-to node combination) and execute the stored procedure which includes SQL codes calculating longest path for given two nodes from referred article

I also created a table to store a path's total weight

Create Table LongestPath_Routes ([weight] decimal(10,1), path varchar(100))

As seen in below SQL script, I clear this table at the beginning. Then populate it for each from-to node set within the stored procedure Finally after cursor execution is completed I query the table by sorting according to weight column for the longest path (also for the shortest path is possible)

truncate table LongestPath_Routes

DECLARE @From TinyInt
DECLARE @To TinyInt

DECLARE PathCursor CURSOR FAST_FORWARD FOR
    select Nodes_From.Id as [From], Nodes_To.Id as [To]
    from LongestPath_Nodes as Nodes_From
    inner join LongestPath_Nodes as Nodes_To
        on Nodes_From.Id <> Nodes_To.Id

OPEN PathCursor

FETCH NEXT FROM PathCursor INTO @From, @To

WHILE @@FETCH_STATUS = 0
BEGIN
set nocount on
 EXEC LongestPath_Calculate_for_Nodes @From, @To
set nocount off

 FETCH NEXT FROM PathCursor INTO @From, @To
END

CLOSE PathCursor
DEALLOCATE PathCursor 

select * from LongestPath_Routes order by [weight] desc

I hope this solution helps you