The best replacement for binary search is linear search.

The best alternatives to binary search are rated as following:
★★★★★  linear search
★★★★  sequential search
★★  merge sort
★★  ternary search
★  quicksort
★  interpolation search
★  hash table
  sequential
  tertiary search

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Speaking about binary search, one probably shouldn't forget about insertion sort.

Other search terms related to binary search and their ratings are:
★★★★★ insertion sort
You have in mind a companion for binary search and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of binary search in all years. Click on graph for more.
binary search
linear search
sequential search