Table 1 Modified bidirectional breadth-first search algorithm

Input: RDF Graph and user query as entity

Output: Semantic Association paths without ranking

/**Path searching for finding all paths at within k hops */

1. Enqueue the root node in the forward queue: the source Thing in the path we want to discover

2. Enqueue the target node in the backward queue: the destination Thing in the path we want to discover

3. Dequeue a forward node and examine it

    a. If the forward node is found in the backward zone//we have met in the middle: quit the search

a.1 If the path passes through user specific intermediate node

return the complete path

a.2 quit the search

    b. Otherwise enqueue any successors that have not yet been examined in the forward queue and add them to the forward zone

4. Dequeue a backward node and examine it

    a. If the backward node is found in the forward zone//we have met in the middle

a.1 If the path passes through user specific intermediate node

return the complete path

a.2 quit the search

    b. Otherwise enqueue any predecessors that have not yet been examined in the backward queue and add them to the backward zone

5. If the any of the two queues is empty, every node on the graph has been examined, quit the search and return "not found"

6. If we are still under the depth limit, repeat from Step 3