The best replacement for backtracking is branch and bound.

The best alternatives to backtracking are rated as following:
★★★★★  branch and bound
★★★★  dynamic programming
★★  greedy

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Speaking about backtracking, one probably shouldn't forget about recursion.

Other search terms related to backtracking and their ratings are:
★★★★★ recursion
★★ n queens problem
★★ 8 queens problem
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Google Trends

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backtracking
branch and bound
dynamic programming