What is the definition of the word "fractional" in algorithms? I have encountered the word in phrases like "fractional algorithm", "fractional node routing problem". I have also encountered the phrase "[...]designing a fractional algorithm and transforming it into a discrete algorithm [...]". Could the word "fractional" mean "continuous"? Could it mean "perfect"?
Note: English is not my native language
I think it's a case of a paper's authors being pretentious. I went digging for some examples, the best I found is this one: http://books.google.com/books?id=X88_R8gH4hsC&lpg=PA54&ots=-FLjG-dNZg&dq=%22fractional%20algorithm%22&pg=PA54#v=onepage&q=%22fractional%20algorithm%22&f=false
The paper writes:
...we show a fractional algorithm for the switch throughput problem, i.e. one that can insert fractions of packets* [...] Then we transform our fractional algorithm into a discrete algorithm, i.e. one that can insert and transit integral packets.
My understanding suggests that a "fractional algorithm" is one that can process sub-integral, but not necessarily continuous (i.e. "a stream") units of data. Obviously this only applies to certain classes of algorithms, but an example could be an image-processing algorithm: a fractional approach might be able to work on an arbitrarily sub-pixel basis rather than per-pixel (i.e. discrete units), but it couldn't necessarily process a stream of color data (e.g. an analog TV scanline).
"Fractional" in the context of algorithms, my research specialty, has a precise technical meaning, namely, when the problem can be formulated in some obvious way as an integer program, the "fractional" version corresponds to the linear program obtained by dropping the integrality constraints. Often it's possible to transform a fractional solution into an integral one by rounding, often in a randomized manner.
