We recently proposed DOVER-Lap, a method for combining overlap-aware speaker diarization system outputs. DOVER-Lap improved upon its predecessor DOVER by using a label mapping method based on globally-informed greedy search. In this paper, we analyze this label mapping in the framework of a maximum orthogonal graph partitioning problem, and present three inferences. First, we show that DOVER-Lap label mapping is exponential in the input size, which poses a challenge when combining a large number of hypotheses. We then revisit the DOVER label mapping algorithm and propose a modification which performs similar to DOVER-Lap while being computationally tractable. We also derive an approximation bound for the algorithm in terms of the maximum number of hypotheses speakers. Finally, we describe a randomized local search algorithm which provides a near-optimal $(1-ε)$-approximate solution to the problem with high probability. We empirically demonstrate the effectiveness of our methods on the AMI meeting corpus. Our code is publicly available: https://github.com/desh2608/dover-lap.