Bansal, Huang, and Lee recently gave a polynomial-time algorithm that colors every $3$-colorable graph on $n$ vertices with $O(n^{0.19539})$ colors. We improve their bound to $O(n^{0.17794})$ colors. The improvement comes from a sharper rule for combining Gaussian covers. We prove the rule from Ehrhard's inequality by...
We give a polynomial-time algorithm that achieves an $\alpha_{GW} + \tilde{\Omega}(1/d)$-approximation for Max 2-LIN(2) in weighted instances where each vertex appears in at most $d$ constraints. This improves on the $\alpha_{GW}+\tilde{\Omega}(1/d^2)$-approximation guarantee of [Hsieh-Kothari, ICALP'23]. We also show...
Rares-Darius Buhai, Suprovat Ghoshal, Pravesh K. Kothari et al.· 0 citations
It is shown that the approximation algorithm for Boolean Max $k$-CSP yields a $(1-o_k(1)/2^k$ approximation, as conjectured in [Makarychev and Makarychev 2017], which improves the previous guarantee of $(0.626612-o_k(1)/2^k$ and asymptotically matches the known hardness results.
The main ingredient is a new algorithm for closing additional centers in parameterized time inspired by local search and the first constant-factor FPT-approximation parameterized by the number of groups $\ell$, resolving the open question raised by Ghadiri, Singh, and Vempala (2022).
Aditya Anand, Yu. S. Makarychev, Liren Shan· 0 citations
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