Re: double linked list
Date: 29 Jan 2003 13:15:51 -0800
Message-ID: <c0d87ec0.0301291315.7ae946eb_at_posting.google.com>
>> The table at hand is more a kind of a collection of graphs where I
want to find all possible paths between a given starting point and a
given end point. <<
For the reachabiity index of a general graph, you need Warshal's algorithm.
Let V = number of nodes in the graph
Let A[i,j] be the adjacency matrix for the undirected graph
FOR j:= 1 TO V
DO FOR i:= 1 TO V
DO IF A[i,j] = 1 THEN FOR k := 1 TO V DO IF A[j,k]] = 1 THEN A[i,k]] := 1;
You can also do a summation to get the length of the path from i to j. You can concatenate names of the nodes into a string that gives the path, etc.
Her is a first attempt at some SQL; I am sure it can be done better
CREATE TABLE Graph
(i CHAR(2) NOT NULL,
j CHAR(2) NOT NULL,
flag CHAR(1) NOT NULL DEFAULT 'n'
CHECK (flag IN ('n', 'y')),
PRIMARY KEY (i,j));
INSERT INTO Graph (i, j, flag)
SELECT DISTINCT G1.i, G2.j, 'y'
FROM Graph AS G1, Graph AS G1
WHERE G1.i <> G2.j
AND EXISTS
(SELECT * FROM Graph AS G3 WHERE G3.i = G1.j AND G3.j = G2.i) AND NOT EXISTS (SELECT * FROM Graph AS G3 WHERE (G3.i = G1.i AND G3.j = G1.j)) OR (G3.i = G2.i AND G3.j = G2.j));
You wll have to run this statement until the size of Graph does not change -- no new rows are being added. Received on Wed Jan 29 2003 - 22:15:51 CET