Opened 4 years ago

Last modified 3 years ago

## #27620 new enhancement

# Addition of Fibonaci Heap for usage in Bidirectional_Dijkstra

Reported by: | HRISHABH YADAV | Owned by: | |
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Priority: | minor | Milestone: | |

Component: | graph theory | Keywords: | |

Cc: | David Coudert | Merged in: | |

Authors: | Reviewers: | ||

Report Upstream: | N/A | Work issues: | |

Branch: | Commit: | ||

Dependencies: | Stopgaps: |

### Description (last modified by )

Like Binomial Heap, Fibonacci Heap is a collection of trees with min-heap or max-heap property:- https://en.wikipedia.org/wiki/Fibonacci_heap. In Fibonacci Heap, trees can have any shape even all trees can be single nodes (This is unlike Binomial Heap where every tree has to be Binomial Tree). Currently, the Fibonacci heap isn't implemented in stl of c++, but Boost has an implementation of https://www.boost.org/doc/libs/1_50_0/doc/html/boost/heap/fibonacci_heap.html

As sage has an interface with Boost, we can have this heap instead of current python heap implemented in Bidirectional_dijkstra. Using Fibonacci Heap we can reduce time complexity of Decrease-Key, which has importance in Dijkstra and Prim algorithms. With Binary Heap, time complexity of these algorithms is O(VLogV + ELogV). If Fibonacci Heap is used, the time complexity is improved to O(VLogV + E).

### Change History (6)

### comment:1 Changed 4 years ago by

### comment:2 Changed 4 years ago by

Priority queue in c++ implements Binomial heap which gives complexity of:

Algorithm Average Worst case Space O(n) O(n) Search O(n) O(n) Insert O(1) O(log n) Delete O(log n) O(log n) Peek O(1) O(1)

whereas Fibonacci Heap reduces complexity Insertion and Decrease key

Algorithm Average Insert Θ(1) Find-min Θ(1) Delete-min O(log n) Decrease-key Θ(1) Merge Θ(1)

### comment:3 Changed 4 years ago by

Type: | PLEASE CHANGE → enhancement |
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### comment:4 Changed 4 years ago by

Description: | modified (diff) |
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### comment:6 Changed 3 years ago by

Milestone: | sage-8.8 |
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