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| Content Provider | ACM Digital Library |
|---|---|
| Author | Khot, Subhash Moshkovitz, Dana |
| Abstract | In this paper, we consider the problem of approximately solving a system of homogeneous linear equations over reals, where each equation contains at most three variables. Since the all-zero assignment always satisfies all the equations exactly, we restrict the assignments to be "non-trivial". Here is an informal statement of our result: it is NP-hard to distinguish whether there is a non-trivial assignment that satisfies 1-δ fraction of the equations or every non-trivial assignment fails to satisfy a constant fraction of the equations with a "margin" of Ω(√δ). We develop linearity and dictatorship testing procedures for functions f: $R^{n}$ -> R over a Gaussian space, which could be of independent interest. We believe that studying the complexity of linear equations over reals, apart from being a natural pursuit, can lead to progress on the Unique Games Conjecture. |
| Starting Page | 413 |
| Ending Page | 420 |
| Page Count | 8 |
| File Format | PDF MP4 |
| ISBN | 9781450306911 |
| DOI | 10.1145/1993636.1993692 |
| Language | English |
| Publisher | Association for Computing Machinery (ACM) |
| Publisher Date | 2011-06-06 |
| Publisher Place | New York |
| Access Restriction | Subscribed |
| Subject Keyword | Hardness of approximation Linear equations Pcp |
| Content Type | Audio Text |
| Resource Type | Article |
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