Dense Subgraphs with Restrictions and Applications to Gene Annotation Graphs

Abstract

Abstract. In this paper, we focus on finding complex annotation patterns representing novel and interesting hypotheses from gene annotation data. We define a generalization of the densest subgraph problem by adding an additional distance restriction (defined by a separate metric) to the nodes of the subgraph. We show that while this generalization makes the problem NP-hard for arbitrary metrics, when the metric comes from the distance metric of a tree, or an interval graph, the problem can be solved optimally in polynomial time. We also show that the densest subgraph problem with a specified subset of vertices that have to be included in the solution can be solved optimally in polynomial time.In addition, we consider other extensions when not just one solution needs to be found, but we wish to list all subgraphs of almost maximum density as well. We apply this method to a dataset of genes and their annotations obtained from The Arabidopsis Information Resource (TAIR). A user evaluation confirms that the patterns found in the distance restricted densest subgraph for a dataset of photomorphogenesis genes are indeed validated in the literature; a control dataset validates that these are not random patterns. Interestingly, the complex annotation patterns potentially lead to new and as yet unknown hypotheses. We perform experiments to determine the properties of the dense subgraphs, as we vary parameters, including the number of genes and the distance.

Finding Cross Genome Patterns in Annotation Graphs

“…We note that while this appears to be a very simple pattern, the association of these two genes and their PO and GO terms annotations represented an as yet unknown and potential interaction between phototropins (PHOT1) and chryptochromes (CRY2) [22].…”

“…PAnG employs our approach in [22] and thus first transforms the tripartite graph G in a weighted bipartite graph G = (A, C, E) where each edge e = (a, c) ∈ E is labeled with the number of nodes b ∈ B that have links to both a and c. We then compute a densest bipartite subgraph G 2 by choosing subsets of A and C to maximize the density of the subgraph. Finally, we build the dense tripartite graph G 3 out of the G 2 by adding all intermediate nodes b ∈ B that are connected to at least one node of G 2 .…”

“…First, we have to find patterns in annotation graph datasets. On this challenge, we can report some initial success [1,22,27].…”

Finding Dense Subgraphs of Sparse Graphs

“…Identifying dense regions of graphs is a fundamental computational problem with many important applications, for instance in computational biology [19] and social network analysis [3]. There are many different definitions of what a dense subgraph is [11,17] and for almost all of these formulations, the corresponding computational problems are NP-hard.…”

InterOnto – Ranking Inter-Ontology Links

“…In [18] Saha et al mine the tripartite graph induced by selected database entries and their annotated ontology concepts for the densest subgraphs. To compute these subgraphs they not only consider the links themselves, but also the distance, i.e., the number of edges between concepts in an ontology, up to a certain threshold.…”