Algorithms Q&A - Recent questions in Branch & Bound

Solve a set of inter-related recurrence relations

Sat, 10 Dec 2022 22:01:12 +0000

T(n) = R(n-1) + n log n
R(n) = T(n-1) + n^2

How can we solve the 8 puzzle problem using Branch & Bound approach?

Tue, 09 Apr 2019 14:57:40 +0000

We want to solve the 8-puzzle, or generally, the n-puzzle (where n is m*m - 1 for some integer) problem. How can we use B&B to solve this problem, and what are the lower/upper bounds?

You are given a Boolean formula involving variables X1, X2, ... Xn.

Sat, 14 Apr 2018 00:05:40 +0000

You are given a Boolean formula involving variables X₁, X₂, ... X_n. The Boolean formula is of form (C₁AND C₂AND C₃... AND C_m), where each clause is a disjunction (logical "or" function) of the X variables. You have to assign true/false values to the variables so as to maximize the number of clauses that evaluate to true. Present a branch and bound approach for this optimization problem.

Given jobs, resources and cost matrix, what assignment minimizes the overall cost?

Mon, 08 May 2017 23:34:51 +0000

2	4	5	3	11
3	5	6	4	8
4	3	5	7	9
3	4	3	8	12
4	2	6	4	9

Given jobs, resources and cost matrix.....for which assignment overall cost is minimum?

The lower bound for the Traveling Salesman Problem

Mon, 05 Dec 2016 22:05:10 +0000

When applying the B&B approach to the Traveling Salesman Problem, we want to minimize the distance (which may satisfy the triangle inequality) or the cost (which may not satisfy the triangle inequality). What is the efficient way to set the lower bound?

I saw from some online resources that we need to consider both the incoming and outgoing edges and their weights, which is either the distance or the cost. We can do a reduction on the weight matrix by subtracting the smallest numbers in each row, and subtracting the smallest numbers in each column, until there is a 0. But I don't quiet understand why is that. Is there other ways to set the lower bounds?

Employee to project assignment reward problem

Mon, 05 Dec 2016 05:35:27 +0000

Describe a Branch & Bound algorithm to solve the employee to project assignment reward problem. You are given n employees and n projects. You are also given an array A[i,j] which contains the revenue realized by that assignment of employee i to project j. Describe your B&B solution to maximize the reward.