Inapproximability of Unique Games in Fixed-Point Logic with Counting
We study the extent to which it is possible to approximate the optimal value of a Unique Games instance in Fixed-Point Logic with Counting (FPC). We prove two new FPC- inexpressibility results for Unique Games: the existence of a \left( {\frac{1}{2},\frac{1}{3} + \delta } \right)-inapproximability g...
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| Vydané v: | Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science s. 1 - 13 |
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29.06.2021
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| Abstract | We study the extent to which it is possible to approximate the optimal value of a Unique Games instance in Fixed-Point Logic with Counting (FPC). We prove two new FPC- inexpressibility results for Unique Games: the existence of a \left( {\frac{1}{2},\frac{1}{3} + \delta } \right)-inapproximability gap, and inapproximability to within any constant factor. Previous recent work has established similar FPC-inapproximability results for a small handful of other problems. Our construction builds upon some of these ideas, but contains a novel technique. While most FPC-inexpressibility results are based on variants of the CFI-construction, ours is significantly different. |
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| AbstractList | We study the extent to which it is possible to approximate the optimal value of a Unique Games instance in Fixed-Point Logic with Counting (FPC). We prove two new FPC- inexpressibility results for Unique Games: the existence of a \left( {\frac{1}{2},\frac{1}{3} + \delta } \right)-inapproximability gap, and inapproximability to within any constant factor. Previous recent work has established similar FPC-inapproximability results for a small handful of other problems. Our construction builds upon some of these ideas, but contains a novel technique. While most FPC-inexpressibility results are based on variants of the CFI-construction, ours is significantly different. |
| Author | Tucker-Foltz, Jamie |
| Author_xml | – sequence: 1 givenname: Jamie surname: Tucker-Foltz fullname: Tucker-Foltz, Jamie email: jtuckerfoltz@gmail.com organization: Harvard University |
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| Snippet | We study the extent to which it is possible to approximate the optimal value of a Unique Games instance in Fixed-Point Logic with Counting (FPC). We prove two... |
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| SubjectTerms | Approximation algorithms Complexity theory Computer science Games Graph theory Linear algebra |
| Title | Inapproximability of Unique Games in Fixed-Point Logic with Counting |
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