Merging Sorted Lists of Similar Strings

Abstract: Merging $T$ sorted, non-redundant lists containing $M$ elements into a single sorted, non-redundant result of size $N \ge M/T$ is a classic problem typically solved practically in $O(M \log T)$ time with a priority-queue data structure the most basic of which is the simple heap. We revisit this problem in the situation where the list elements are strings and the lists contain many identical or nearly identical elements. By keeping simple auxiliary information with each heap node, we devise an $O(M \log T+S)$ worst-case method that performs no more character comparisons than the sum of the lengths of all the strings $S$, and another $O(M \log (T/ \bar e)+S)$ method that becomes progressively more efficient as a function of the fraction of equal elements $\bar e = M/N$ between input lists, reaching linear time when the lists are all identical. The methods perform favorably in practice versus an alternate formulation based on a trie.