What is the difference between divide and conquer, and branch and reduce.
From Exact Exponential Algorithms by Fomin and Kratsch, branch and reduce algorithms uses two types of rules:
- A reduction rule is used to simplify a problem instance or halt the algorithm
- A branching rule is used to solve a problem instance by recursively solving smaller instances of a problem.
To me this sounds a lot like the definition of divide and conquer given on Wikipedia:
divide and conquer (D&C) is an algorithm design paradigm based on multi-branched recursion. A divide and conquer algorithm works by recursively breaking down a problem into two or more sub-problems of the same or related type, until these become simple enough to be solved directly.
However when comparing branch and reduce algorithms, like k-satisfiability or computing a maximum independent set, to divide and conquer algorithms, like quicksort and merge sort, they do not feel the same to me.
So is there a difference between divide and conquer, and branch and reduce? If so, what characteristic makes them different.
