An approximation algorithm for the balanced Max-3-Uncut problem using complex semidefinite programming rounding

Graph partition problems have been investigated extensively in combinatorial optimization. In this work, we consider an important graph partition problem which has applications in the design of VLSI circuits, namely, the balanced Max-3-Uncut problem. We formulate the problem as a discrete linear program with complex variables and propose an approximation algorithm with an approximation ratio of 0.3456 using a semidefinite programming rounding technique along with a greedy swapping step afterwards to guarantee the balanced constraint. Our analysis utilizes a bivariate function, rather than the univariate function in previous work.