摘要：Using outward rotations, we obtain an approximation algorithm for MAXn/2-UNCUT problem, i.e., partitioning the vertices of a weighted graph into two blocks of equalcardinality such that the total weight of edges that do not cross the cut is maximized. In manyinteresting cases, the algorithm performs better than the algorithms of Ye and of Halperin andZwick. The main tool used to obtain this result is semidefinite programming.

摘要：The use of a reconfigurable intelligent surface(RIS)in the enhancement of the rate performance is considered to involve the limitation of the RIS being a passive *** address this issue,we propose a RIS-aided amplify-and-forward(AF)relay network in this *** jointly optimizing the beamforming matrix at AF relay and the phase-shift matrices at RIS,two schemes are put forward to address a maximizing signal-to-noise ratio(SNR)***,aiming at achieving a high rate,a high-performance alternating optimization(AO)method based on Charnes–Cooper transformation and semidefinite programming(CCT-SDP)is proposed,where the optimization problem is decomposed into three subproblems solved using CCT-SDP,and rank-one solutions can be recovered using Gaussian ***,the optimization variables in the CCT-SDP method are matrices,leading to extremely high *** reduce the complexity,a low-complexity AO scheme based on Dinkelbachs transformation and successive convex approximation(DT-SCA)is proposed,where the variables are represented in vector form,and the three decoupling subproblems are solved using *** results verify that compared to three benchmarks(i.e.,a RIS-assisted AF relay network with random phase,an AF relay network without RIS,and a RIS-aided network without AF relay),the proposed CCT-SDP and DT-SCA schemes can harvest better rate ***,it is revealed that the rate of the low-complexity DT-SCA method is close to that of the CCT-SDP method.