[Radim]

Cache + avoid dynamic allocations like the plague. For example, high-perf search algos implement reversible transitions: instead of creating & pushing new states around all the time, modify just one state, in-place. And then apply the same transformation in reverse when backtracking.

If you design your data structures well – to reflect the required transitions and query operations, rather than what the problem looks like to a human when drawn on a piece of paper – the forward/backward transition is nearly a no-op. Just some binary bit fiddling over data that's already in a CPU cache. And there's NO DYNAMIC ALLOCATIONS at all. Your search will fly!

The OP also mentions another great "caching" technique, under "Entropy reduction". This is really hard but basically try to find symmetries in the search space which allow you to prune away entire subspaces apriori, without searching at all. Often it'll be something like "rotating by 90 degrees leads to the same position", mirror positions, invariance to color, time… the symmetry types and their runtime benefits are problem-specific, so you need to sit and think hard about what makes a solution unique.

In the limit, you may be lucky enough to prune away so much of the solution space that there's only a single state left. Congratulations: you've solved the problem analytically :)