# Definition of fractional in theoretical CS

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

• 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 May 2 '14 at 22:56
• 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 ceid.upatras.gr/webpages/courses/approx/book.pdf – Helium May 3 '14 at 9:44
• 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 May 3 '14 at 14:58

## 1 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'.