Dijkstra's shortest path algorithm â¢ This algorithm is a âgreedyâ one ...

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Priority Queues• A priority queue is a list of items in which each item has associated with ita priority. In general, different items may have different priorities and wespeak of one item having a higher priority than another. Given such a listwe can determine which is the highest (or the lowest) priority item in thelist. Items are inserted into a priority queue in any, arbitrary order. However,items are withdrawn from a priority queue in order of their prioritiesstarting with the highest (lowest) priority item first.• For example, consider the software which manages a printer. In general, itis possible for users to submit documents for printing much more quicklythan it is possible to print them. A simple solution is to place the documentsin a FIFO queue. In a sense this is fair, because the documents are printedon a first-come, first-served basis.• However, a user who has submitted a short document for printing willexperience a long delay when much longer documents are already in thequeue. An alternative solution is to use a priority queue in which the shortera document, the higher its priority. By printing the shortest documents first,we reduce the level of frustration experienced by the users. In fact, it canbe shown that printing documents in order of their length minimizes theaverage time a user waits for her document.• Removing a job with the smallest number of pages can be done with EXTRACT-MIN.• You also need to be able to insert a new item into the queue (e.g., whenfirst building the set Q in Dijkstra).12
Insertion Operation• Insert 14; make a “hole” at the end of the array• Move the hole up to the “proper” position, then insert the 1413
Page 5: The inductive step of Dijkstra• T
Page 11: Ultimate effect on complexity of DI
Page 15 and 16: Proving correctness of FLOYD-WARSHA
Page 17: How do you prove that there isn’t

Dijkstra's shortest path algorithm â¢ This algorithm is a âgreedyâ one ...

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Dijkstra's shortest path algorithm â¢ This algorithm is a âgreedyâ one ...