Motivation: Estimated gene trees are often inaccurate, due to insufficient phylogenetic signal in the single gene alignment, among other causes. Gene tree correction aims to improve the accuracy of an estimated gene tree by using computational techniques along with auxiliary information, such as a reference species tree or sequencing data. However, gene trees and species trees can differ as a result of gene duplication and loss (GDL), incomplete lineage sorting (ILS), and other biological processes. Thus gene tree correction methods need to take estimation error as well as gene tree heterogeneity into account. Many prior gene tree correction methods have been developed for the case where GDL is present. Results: Here, we study the problem of gene tree correction where gene tree heterogeneity is instead due to ILS and/or HGT. We introduce TRACTION, a simple polynomial time method that provably finds an optimal solution to the RF-optimal tree refinement and completion (RF-OTRC) Problem, which seeks a refinement and completion of a singlylabeled gene tree with respect to a given singly-labeled species tree so as to minimize the Robinson−Foulds (RF) distance. Our extensive simulation study on 68,000 estimated gene trees shows that TRACTION matches or improves on the accuracy of well-established methods from the GDL literature when HGT and ILS are both present, and ties for best under the ILS-only conditions. Furthermore, TRACTION ties for fastest on these datasets. We also show that a naive generalization of the RF-OTRC problem to multi-labeled trees is possible, but can produce misleading results where gene tree heterogeneity is due to GDL.

We present a hierarchical skeleton-guided motion planning algorithm to guide mobile robots. A good skeleton maps the connectivity of the subspace of c-space containing significant degrees of freedom and is able to guide the planner to find the desired solutions fast. However, sometimes the skeleton does not closely represent the free c-space, which often misleads current skeleton-guided planners. The hierarchical skeleton-guided planning strategy gradually relaxes its reliance on the workspace skeleton as C space is sampled, thereby incrementally returning a sub-optimal path, a feature that is not guaranteed in the standard skeleton-guided algorithm. Experimental comparisons to the standard skeleton guided planners and other lazy planning strategies show significant improvement in roadmap construction run time while maintaining path quality for multi-query problems in cluttered environments.