We investigate a special case of the graph partitioning problem: the partitioning of a sibling graph which is an ordered tree augmented with edges connecting consecutive nodes that share a common parent. We describe the algorithm, XS, and present a proof of its correctness. © 2008 Elsevier B.V. All rights reserved.
Bordawekar, R., & Shmueli, O. (2008). An algorithm for partitioning trees augmented with sibling edges. Information Processing Letters, 108(3), 136–142. https://doi.org/10.1016/j.ipl.2008.04.010