Better balance by being biased: A 0.8776-approximation for max bisection
Per Austrin, Siavosh Benabbas, Konstantinos Georgiou · 2013
Recently Raghavendra and Tan (SODA 2012) gave a 0.85-approximation algorithm for the Max Bisection problem. We improve their algorithm to a 0.8776-approximation. As Max Bisection is hard to approximate within αGW+ ≈ 0.8786 under the Unique Games Conjecture (UGC), our algorithm is nearly optimal. We conjecture that Max Bisection is approximable within αGW −, i.e., that the bisection constraint (essentially) does not make Max Cut harder. We also obtain an optimal algorithm (assuming the UGC) for the analogous variant of Max 2-Sat. Our approximation ratio for this problem exactly matches the optimal approximation ratio for Max 2-Sat, i.e., αLLZ + ≈ 0.9401, showing that the bisection constraint does not make Max 2-Sat harder. This improves on a 0.93-approximation for this problem due to Raghavendra and Tan. 1 ar