The tag has no usage guidance.

learn more… | top users | synonyms

3
votes
0answers
46 views

Branch and Bound running time and golden ratio

This is a follow up question to When does Branch and Bound exactly stop giving solutions for the bin packing problem After testing many instances I found out that when r = V / Vtotal <= ϕ (Golden ...
1
vote
0answers
91 views

When does Branch and Bound exactly stop giving solutions for the bin packing problem

I wrote a branch and bound algorithm for the bin packing problem and now I would like to know when exactly it stops giving solutions in a polynomial time. I have N items (each item i has a volume ...
1
vote
1answer
65 views

Matching a set of paths to an incrementally generated graph

I am working on an approximate matching problem, where I have a set of paths in an unknown graph (A) and a partial graph (B), where B is generated incrementally during the matching process (and can be ...
4
votes
1answer
140 views

Making a branch-and-bound algorithm more efficient for a large input

I am trying to implement the branch and bound algorithm to solve the knapsack problem (in the Coursera discrete optimisation course). I tried implementing dynamic programming first, and that worked ...
1
vote
2answers
625 views

How to find the Branch factor of 8 Puzzle

I would like to know how to find the average branching factor for 8 puzzle.While referring Artificial Intelligence by George F Luger it says that: Suppose,for example we wish to establish the ...
1
vote
1answer
123 views

Can the effective branching factor be negative?

I've implemented A* algorithm in Python, after that I calculated the effective branching factor $ B^* $ $$ T+1=1+B^*+(B^*)^2+\dots +(B^*)^L$$ where $T$ is the number of expanded nodes. My question ...
1
vote
1answer
55 views

How does the Vertex Cover algorithm by Chen et al find its tuples?

I'm still fighting with the aforementioned paper "Improved upper bounds for vertex cover" by Chen, Kanj, Xia (PDF kindly provided by Yuval Filmus). My current problem is that it's specified that the ...
2
votes
1answer
340 views

Traveling Salesman: how to use a lower bound?

Let me preface this question by giving some helpful background material. I'm trying to solve the traveling salesman problem using branch and bound. Concretely, for a partial solution, I'm using the ...
2
votes
0answers
223 views

Trying to understand the Gilmore-Lawler lower bound

For a class project we're developing a software that solves a common optimisation problem. After some research we've found out that our problem is called QAP (Quadratic Asssignment Problem) and the ...
4
votes
3answers
2k views

What is the difference between bounding and pruning in branch-and-bound algorithms?

Could anybody please explain what the difference between "bounding" and "pruning" in branch and bound algorithms is? I'd also appreciate references (preferably books), where this distinction is made ...
8
votes
2answers
5k views

Branch and Bound explanation

I have a test about the branch and bound algorithm. I understand theoretically how this algorithm works but I couldn't find examples that illustrates how this algorithm can be implemented practically. ...