Finding a path in 2 dimensional array

Question

I have MySQL database with no constraints definition and I also have a multidimensional array in PHP which contains information about tables relations in this database. The array is in this format (only an example):

array(20){
    ps_attribute_lang => array(2) {
      id_attribute => array(2) {
         totable => "ps_attribute" (12)
         tocolumn => "id_attribute" (12)
      }
      id_lang => array(2) {
         totable => "ps_lang" (7)
         tocolumn => "id_lang" (7)
      }
    }
    ps_cart => array(4) {
      id_lang => array(2) {
         totable => "ps_lang" (7)
         tocolumn => "id_lang" (7)
      }
      id_address_delivery => array(2) {
         totable => "ps_address" (10)
         tocolumn => "id_address" (10)
      }
      id_address_invoice => array(2) {
         totable => "ps_address" (10)
         tocolumn => "id_address" (10)
      }
      id_customer => array(2) {
         totable => "ps_customer" (11)
         tocolumn => "id_customer" (11)
      }
    }
    ps_cart_product => array(1) {
      id_product => array(2) {
         totable => "ps_product" (10)
         tocolumn => "id_product" (10)
      }
    }
 ...
}

Now I'm wondering how can one find a path in this database from one table to another.

Let me give an example. Let's say we have following tables in our database:

• states(id_state, name)
• cities(id_city, id_state, name)
• streets(id_street, id_city, name)
• houses(id_house, id_street, color, number)
• people(id_house, name)

Now let's say that each time I want to find house with some properties (e.g. every blue house that resides in Chicago). For this I need to generate SQL command.¨

SELECT part of SQL is simple (e.g. SELECT houses.id). WHERE part of SQL is also very simple (e.g. WHERE cities.name = 'Chicago' AND house.color = 'blue'). The problem is in "connecting" tables in JOIN part of SQL.

I simply need to search this multidimensional relations array and find a path that connects all tables that contain conditions from WHERE part of SQL AND SELECT part of SQL.

In this case I want to get this:

SELECT house.id
FROM house
JOIN street ON(house.id_street = street.id)
JOIN city ON(street.id_city = city.id)
WHERE house.color = 'blue' AND city.name = 'chicago'

Do you know any algorithm that is capable of getting this kind of info from this structure?

Thank you in advance!