A generalization of hierarchical exchangeability on trees to directed acyclic graphs

Hierarchical alignment of weighted directed acyclic graphs

In some applications of matching, the structural or hierarchical properties of the two graphs being aligned must be maintained. The hierarchical properties are induced by the direction of the edges in the two directed graphs. These structural relationships defined by the hierarchy in the graphs act as a constraint on the alignment. In this paper, we formalize this problem as the weighted alignm...

Cost-minimal trees in directed acyclic graphs

A number of examples are given where one seeks a minimal-cost tree to span a given subset of the nodes of a connected, directed, acyclic graph (we call such a graph monotonic). Some of these examples require an al~orithm to transform the problem into the form of a minimization problem in a monotonic graph.; this algorithm is also given. Finally, an implicit enumeration algorithm is presented fo...

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. The size is linear in the number of nodes. We also consider a “fuzzy” variant of LSCA that allows to compute a node that is only an LSCA of a given perc...

Lowest common ancestors in trees and directed acyclic graphs

We study the problem of finding lowest common ancestors (LCA) in trees and directed acyclic graphs (DAGs). Specifically, we extend the LCA problem to DAGs and study the LCA variants that arise in this general setting. We begin with a clear exposition of Berkman and Vishkin’s simple optimal algorithm for LCA in trees. Their ideas lay the foundation for our work on LCA problems in DAGs. We presen...

Generic Directed Acyclic Graphs