SETH vs Approximation
ACM SIGACT News(2019)
摘要
Our story is about hardness of problems in P, but its roots begin with two algorithmic approaches that have been developed to cope with NP-hard problems: approximation algorithms and fasterthan- brute-force algorithms.
Approximation algorithms were proposed as a response for NP-hardness almost immediately (in historical perspective of almost half a century), and have been one of the most celebrated success stories of our eld. An outstanding complexity result in this area, which has since turned into a sub- eld of its own, is the Probabilistically Checkable Proof (PCP) Theorem. For many problems like Max-3-SAT we now have nearly tight hardness-of-approximation results.
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