Question

As a programming exercise, I just finished writing a Sudoku solver that uses the backtracking algorithm (see Wikipedia for a simple example written in C).

To take this a step further, I would like to use Snow Leopard’s GCD to parallelize this so that it runs on all of my machine’s cores. Can someone give me pointers on how I should go about doing this and what code changes I should make? Thanks!

Matt

Answer 1

For one, since backtracking is a depth-first search it is not directly parallelizable, since any newly computed result cannot be used be directly used by another thread. Instead, you must divide the problem early, i.e. thread #1 starts with the first combination for a node in the backtracking graph, and proceeds to search the rest of that subgraph. Thread #2 starts with the second possible combination at the first and so forth. In short, for n threads find the n possible combinations on the top level of the search space (do not “forward-track”), then assign these n starting points to n threads.

However I think the idea is fundamentally flawed: Many sudoku permutations are solved in a matter of a couple thousands of forward+backtracking steps, and are solved within milliseconds on a single thread. This is in fact so fast that even the small coordination required for a few threads (assume that n threads reduce computation time to 1/n of original time) on a multi-core/multi-CPU is not negligible compared to the total running time, thus it is not by any chance a more efficient solution.