<p>The most common use of 'fractional' is when you're solving an integer program. You relax it by dropping the constraints that the solution be integers, thus yielding a <strong>linear</strong> program in which the variables can take <strong>fractional</strong> values (fractional comes from fraction). Later, you can convert the fractional values into integers via a process called 'rounding'. </p>

CC BY-SA 3.0
2014-05-02T23:38:25.480Z
2014-05-02T23:38:25.480Z
Suresh Venkat
<p>What is the definition of the word "fractional" in algorithms? I have encountered the word in phrases like "fractional algorithm", "fractional node routing problem".</p>

<p>Note: English is not my native language</p>

CC BY-SA 3.0
2014-05-02T22:56:34.850Z
I have also encountered the phrase "[...]designing a fractional algorithm and transforming it into a discrete algorithm [...]". Could the word "fractional" mean "continuous"?
George Tseres
CC BY-SA 3.0
2014-05-03T09:44:48.273Z
Suresh's answer is correct. See Chapter 11 of Vazirani's Approximation algorithms book for an example of such algorithms. The book is available at https://www.ceid.upatras.gr/webpages/courses/approx/book.pdf
Helium
CC BY-SA 3.0
2014-05-03T14:58:32.330Z
there is also a sense of "fractional" wrt graphs referring to hypergraphs. use of the term presumably is broad and does not have a fully general crosscutting concept or definition.
vzn
<graph-algorithms><online-algorithms>
Definition of fractional in theoretical CS
George Tseres
# Definition of fractional in theoretical CS

(Asked by: username_0 on 2014-05-02)

What is the definition of the word "fractional" in algorithms? I have encountered the word in phrases like "fractional algorithm", "fractional node routing problem".

Note: English is not my native language

**Tags:** graph-algorithms, online-algorithms

> **Comments:**
> **username_0**: I have also encountered the phrase "[...]designing a fractional algorithm and transforming it into a discrete algorithm [...]". Could the word "fractional" mean "continuous"?  
> **username_1**: Suresh's answer is correct. See Chapter 11 of Vazirani's Approximation algorithms book for an example of such algorithms. The book is available at https://www.ceid.upatras.gr/webpages/courses/approx/book.pdf  
> **username_2**: there is also a sense of "fractional" wrt graphs referring to hypergraphs. use of the term presumably is broad and does not have a fully general crosscutting concept or definition.  

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## 1 answers

### Answer by username_3 on 2014-05-02. Score: 10 | Accepted answer

The most common use of 'fractional' is when you're solving an integer program. You relax it by dropping the constraints that the solution be integers, thus yielding a **linear** program in which the variables can take **fractional** values (fractional comes from fraction). Later, you can convert the fractional values into integers via a process called 'rounding'.


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