Median String Problem with Unbounded Alphabets (Median String Problem)

From Algorithm Wiki
Revision as of 13:03, 15 February 2023 by Admin (talk | contribs)
Jump to navigation Jump to search

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 Decades graph

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

References/Citation

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

Retrieved from "https://algorithm-wiki-csail-mit-edu.ezproxy.canberra.edu.au/w/index.php?title=Median_String_Problem_with_Unbounded_Alphabets&oldid=46214"