The unique games conjecture states that for every sufficiently small pair of constants ε, δ > 0, there exists a constant k such that the following promise problem (Lyes, Lno) is NP-hard:
- Lyes = {G: the value of G is at least 1 − δ}
- Lno = {G: the value of G is at most ε}
where G is a unique game whose answers come from a set of size k.
Read more about Unique Games Conjecture: Relevance, Discussion and Alternatives
Famous quotes containing the words unique, games and/or conjecture:
“An absolute can only be given in an intuition, while all the rest has to do with analysis. We call intuition here the sympathy by which one is transported into the interior of an object in order to coincide with what there is unique and consequently inexpressible in it. Analysis, on the contrary, is the operation which reduces the object to elements already known.”
—Henri Bergson (1859–1941)
“At the age of twelve I was finding the world too small: it appeared to me like a dull, trim back garden, in which only trivial games could be played.”
—Elizabeth Bowen (1899–1973)
“What these perplexities of my uncle Toby were,—’tis impossible for you to guess;Mif you could,—I should blush ... as an author; inasmuch as I set no small store by myself upon this very account, that my reader has never yet been able to guess at any thing. And ... if I thought you was able to form the least ... conjecture to yourself, of what was to come in the next page,—I would tear it out of my book.”
—Laurence Sterne (1713–1768)