使用斐波那契堆改进 Dijkstra？

Question

我发现 this implementation（相关部分如下）Dijkstra 使用优先级队列。是否可以通过实施 Fibonacci 堆甚至移动到迭代深化 A* 来进一步加快速度？

 47     public static void computePaths(Vertex source)
 48     {
 49         source.minDistance = 0.;
 50         PriorityQueue<Vertex> vertexQueue = new PriorityQueue<Vertex>();
 51     vertexQueue.add(source);
 52 
 53     while (!vertexQueue.isEmpty()) {
 54         Vertex u = vertexQueue.poll();
 55 
 56             // Visit each edge exiting u
 57             for (Edge e : u.adjacencies)
 58             {
 59                 Vertex v = e.target;
 60                 double weight = e.weight;
 61                 double distanceThroughU = u.minDistance + weight;
 62         if (distanceThroughU < v.minDistance) {
 63             vertexQueue.remove(v);
 64 
 65             v.minDistance = distanceThroughU ;
 66             v.previous = u;
 67             vertexQueue.add(v);
 68         }
 69             }
 70         }
 71     }

Answer 1

是的，你可以。

建议的实施存在重大性能缺陷：

 62         if (distanceThroughU < v.minDistance) {
 63             vertexQueue.remove(v);
 64 
 65             v.minDistance = distanceThroughU ;
 66             v.previous = u;
 67             vertexQueue.add(v);
 68         }

这段代码的问题在于，从优先级队列中移除任意（非根）节点 v 是在线性时间内完成的。 Java Docs:

Implementation note: this implementation provides O(log(n)) time for the enqueing and dequeing methods (offer, poll, remove() and add); linear time for the remove(Object) and contains(Object) methods; and constant time for the retrieval methods (peek, element, and size).

然而，在斐波那契堆中，您可以更有效地更改节点的优先级。

使用斐波那契堆改进 Dijkstra？

Improving on Dijkstra using Fibonacci heaps?

java

algorithm

path-finding