Difference between Dijkstra Algorithm: Priority Queue vs. Runtime Doubly Linked List

Question

What is the difference in complexity of execution between the following and why ?:

(1) DIJKSTRA algorithm using a regular priority queue (heap)

(2) DIJKSTRA algorithm using a doubly linked list

(If there is no difference)

Answer 1

The most common version of Dijkstra's algorithm assumes that you have access to some kind of priority queue structure that supports the following operations:

• make-heap (s, n): n & infin;, node s, 0.
• dequeue-min(): .
• reduce-key (obj, key): obj , .

Dijkstra make-heap, O (n) dequeue-min, O (m) , n - , m - . O (T _mh + nT _deq + mT _dk), T _mh, T _deq, T _dk - () make-heap, dequeue .

, . : . .

- O (n): node, n - 1 . dequeue-min - O (1): . - O (n), node, , , , , ( case), . , O (n + n + nm) = O (mn).

O (n), n . dequeue-min O (n), , . O (1), node . , O (n + n ² + m) = O (n ² + m) = O (n ²), O (n ²). .

O (n), heapify . - O (log n), - O (log n) ( ). , O (n + n log n + m log n) = O (m log n), , m & ge; .

. , . make- O (n), dequeue-min O (log n) - () O (1) . O (n + n log n + m) = O (m + n log n), , .

, ! . , " " , , .