Median String Problem with Unbounded Alphabets (Median String Problem)

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Description

Given an unbounded alphabet $\Sigma$, a set $W$ of strings over $\Sigma$, and the Levenshtein distance between strings, find a string over $\Sigma$ that minimizes the sum of distances to the strings of $W$.

Related Problems

Related: Median String Problem with Bounded Alphabets, Median String Problem with Binary Alphabets

Parameters

n: number of strings

Table of Algorithms

Name Year Time Space Approximation Factor Model Reference
Naive Solution 1965 {2}^$O(n)$ $O(n)$ auxiliary Exact Deterministic

Time Complexity Graph

Median String Problem - Median String Problem with Unbounded Alphabets - Time.png

Space Complexity Graph

Median String Problem - Median String Problem with Unbounded Alphabets - Space.png

Pareto Frontier Improvements Graph

Median String Problem - Median String Problem with Unbounded Alphabets - Pareto Frontier.png

References/Citation

https://link.springer.com/content/pdf/10.1007/3-540-44888-8_23.pdf

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