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15.082 and 6.855J February 25, 2003 Radix Heap Animation.

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Presentation on theme: "15.082 and 6.855J February 25, 2003 Radix Heap Animation."— Presentation transcript:

1 and 6.855J February 25, 2003 Radix Heap Animation

2 2  An Example from AMO (with a small change) Initialize distance labels Insert nodes into buckets. Initialize buckets and their ranges.   

3 3  Select Select the node with minimum distance label   

4 4  Update Scan arcs out of node 1 and update distance labels.   

5 5  Select Select the node with minimum distance label  Node 3 has label 0, which is minimum

6 6  Update Scan arcs out of node 3 and update distance labels. 

7 7  Select: part Find the first non-empty bucket, by scanning buckets from left to right. 

8 8  Select: part Determine the minimum distance value in the bucket, by scanning all nodes in the bucket.  d(5) = 9, which is minimum.

9 9  Select: part Redistribute the range of bucket 5 into the first 4 buckets, starting with value 9. Bucket widths stay the same, except that some may be smaller.  

10 10  Select: part Reinsert nodes in the correct bucket. Determine the bucket by scanning left.   At this point the leftmost bucket is non-empty

11 11  Select: part Select a node in the leftmost bucket.  

12 12  Update Scan arcs out of node 5 and update distance labels.   Reinsert nodes in correct buckets by scanning left.

13 13 Select: parts 1 and Find the minimum non-empty bucket.   Find the minimum distance label in the bucket

14 14 Select: parts 3 and Redistribute bucket ranges in the minimum bucket   Reinsert nodes in correct buckets. 

15 Select: part Select a node from the leftmost bucket.   

16 16 Update Scan the arc out of node 2.   

17 17 Select, Modified rule Find the minimum non-empty bucket    If the bucket has a width of 1, select any node in the bucket. 4

18 18 Update Scan the arc out of node 4   

19 19 Select: modified rule Find the minimum non-empty bucket    If the bucket has a single node, then select the node. 6 Modified rules and heuristics often help in practice, but must be used carefully.

20 20 The algorithm ends There are no arcs to update.   5 17  There are no nodes that need to be permanently labeled. 6


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