What is the meaning of 'breadth' in breadth first search?












1












$begingroup$


I was learning about breadth first search and a question came in my mind that why BFS is called so. In the book Introduction to Algorithms by CLRS, I read the following reason for this:




Breadth-first search is so named because it expands the frontier
between discovered and undiscovered vertices uniformly across the
breadth of the frontier.




However, I'm not able to understand the meaning of this statement. I'm confused about this word "frontier" and breadth of that frontier.



So, can someone please answer this question in a way which is easy to understand for a beginner like me?






graphs graph-theory shortest-path graph-traversal







share|cite|improve this question











$endgroup$

















    1












    $begingroup$


    I was learning about breadth first search and a question came in my mind that why BFS is called so. In the book Introduction to Algorithms by CLRS, I read the following reason for this:




    Breadth-first search is so named because it expands the frontier
    between discovered and undiscovered vertices uniformly across the
    breadth of the frontier.




    However, I'm not able to understand the meaning of this statement. I'm confused about this word "frontier" and breadth of that frontier.



    So, can someone please answer this question in a way which is easy to understand for a beginner like me?






    graphs graph-theory shortest-path graph-traversal







    share|cite|improve this question











    $endgroup$















      1












      1








      1





      $begingroup$


      I was learning about breadth first search and a question came in my mind that why BFS is called so. In the book Introduction to Algorithms by CLRS, I read the following reason for this:




      Breadth-first search is so named because it expands the frontier
      between discovered and undiscovered vertices uniformly across the
      breadth of the frontier.




      However, I'm not able to understand the meaning of this statement. I'm confused about this word "frontier" and breadth of that frontier.



      So, can someone please answer this question in a way which is easy to understand for a beginner like me?






      graphs graph-theory shortest-path graph-traversal







      share|cite|improve this question











      $endgroup$




      I was learning about breadth first search and a question came in my mind that why BFS is called so. In the book Introduction to Algorithms by CLRS, I read the following reason for this:




      Breadth-first search is so named because it expands the frontier
      between discovered and undiscovered vertices uniformly across the
      breadth of the frontier.




      However, I'm not able to understand the meaning of this statement. I'm confused about this word "frontier" and breadth of that frontier.



      So, can someone please answer this question in a way which is easy to understand for a beginner like me?






      graphs graph-theory shortest-path graph-traversal




      graphs graph-theory shortest-path graph-traversal






      share|cite|improve this question















      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited 1 hour ago







      DG4

















      asked 2 hours ago









      DG4DG4

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      1135






















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          $begingroup$

          Consider the data structure used to represent the search. In a BFS, you use a queue. If you come across an unseen node, you add it to the queue.



          The “frontier” is the set of all nodes in the search data structure. The queue will will iterate through all nodes on the frontier sequentially, thus iterating across the breadth of the frontier. DFS will always pop the most recently discovered state off of the stack, thus always iterating over the deepest part of the frontier.



          Consider the image below. Notice how the DFS goes straight to the deepest parts of the tree whereas BFS iterates over the breadth of each level.



          dfs bfs



          Image here






          share|cite|improve this answer








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            1 Answer
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            active

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            $begingroup$

            Consider the data structure used to represent the search. In a BFS, you use a queue. If you come across an unseen node, you add it to the queue.



            The “frontier” is the set of all nodes in the search data structure. The queue will will iterate through all nodes on the frontier sequentially, thus iterating across the breadth of the frontier. DFS will always pop the most recently discovered state off of the stack, thus always iterating over the deepest part of the frontier.



            Consider the image below. Notice how the DFS goes straight to the deepest parts of the tree whereas BFS iterates over the breadth of each level.



            dfs bfs



            Image here






            share|cite|improve this answer








            New contributor




            Bryce Kille is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
            Check out our Code of Conduct.






            $endgroup$


















              3












              $begingroup$

              Consider the data structure used to represent the search. In a BFS, you use a queue. If you come across an unseen node, you add it to the queue.



              The “frontier” is the set of all nodes in the search data structure. The queue will will iterate through all nodes on the frontier sequentially, thus iterating across the breadth of the frontier. DFS will always pop the most recently discovered state off of the stack, thus always iterating over the deepest part of the frontier.



              Consider the image below. Notice how the DFS goes straight to the deepest parts of the tree whereas BFS iterates over the breadth of each level.



              dfs bfs



              Image here






              share|cite|improve this answer








              New contributor




              Bryce Kille is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
              Check out our Code of Conduct.






              $endgroup$
















                3












                3








                3





                $begingroup$

                Consider the data structure used to represent the search. In a BFS, you use a queue. If you come across an unseen node, you add it to the queue.



                The “frontier” is the set of all nodes in the search data structure. The queue will will iterate through all nodes on the frontier sequentially, thus iterating across the breadth of the frontier. DFS will always pop the most recently discovered state off of the stack, thus always iterating over the deepest part of the frontier.



                Consider the image below. Notice how the DFS goes straight to the deepest parts of the tree whereas BFS iterates over the breadth of each level.



                dfs bfs



                Image here






                share|cite|improve this answer








                New contributor




                Bryce Kille is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                Check out our Code of Conduct.






                $endgroup$



                Consider the data structure used to represent the search. In a BFS, you use a queue. If you come across an unseen node, you add it to the queue.



                The “frontier” is the set of all nodes in the search data structure. The queue will will iterate through all nodes on the frontier sequentially, thus iterating across the breadth of the frontier. DFS will always pop the most recently discovered state off of the stack, thus always iterating over the deepest part of the frontier.



                Consider the image below. Notice how the DFS goes straight to the deepest parts of the tree whereas BFS iterates over the breadth of each level.



                dfs bfs



                Image here







                share|cite|improve this answer








                New contributor




                Bryce Kille is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                Check out our Code of Conduct.









                share|cite|improve this answer



                share|cite|improve this answer






                New contributor




                Bryce Kille is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                Check out our Code of Conduct.









                answered 1 hour ago









                Bryce KilleBryce Kille

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                565




                New contributor




                Bryce Kille is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                Check out our Code of Conduct.





                New contributor





                Bryce Kille is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                Check out our Code of Conduct.






                Bryce Kille is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                Check out our Code of Conduct.






























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