New common ancestor problems in trees and directed acyclic graphs

We derive a new generalization of lowest common ancestors (LCAs) in dags, called the lowest single common ancestor (LSCA). We show how to preprocess a static dag in linear time such that subsequent LSCA-queries can be answered in constant time. We also consider a “fuzzy” variant of LSCA that allows to compute a node that is only an LSCA of a given percentage of the query nodes. The space and construction time of our scheme for fuzzy LSCAs is linear, whereas the query time has a sub-logarithmic slow-down. This “fuzzy” algorithm is also applicable to LCAs in trees, with the same complexities. Key words: Algorithms, Data Structures, Computational Biology

• Type: Journal
• Year: 2010
• Where: IPL
• Authors: Johannes Fischer, Daniel H. Huson
• Keywords: Common Ancestor, IPL 2010, Lowest Common Ancestors, Single Common Ancestor