004 Datenverarbeitung; Informatik
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Coherent network partitions
(2021)
We continue to study coherent partitions of graphs whereby the vertex set is partitioned into subsets that induce biclique spanned subgraphs. The problem of identifying the minimum number of edges to obtain biclique spanned connected components (CNP), called the coherence number, is NP-hard even on bipartite graphs. Here, we propose a graph transformation geared towards obtaining an O (log n)-approximation algorithm for the CNP on a bipartite graph with n vertices. The transformation is inspired by a new characterization of biclique spanned subgraphs. In addition, we study coherent partitions on prime graphs, and show that finding coherent partitions reduces to the problem of finding coherent partitions in a prime graph. Therefore, these results provide future directions for approximation algorithms for the coherence number of a given graph.
PC2P
(2021)
Motivation:
Prediction of protein complexes from protein-protein interaction (PPI) networks is an important problem in systems biology, as they control different cellular functions. The existing solutions employ algorithms for network community detection that identify dense subgraphs in PPI networks. However, gold standards in yeast and human indicate that protein complexes can also induce sparse subgraphs, introducing further challenges in protein complex prediction.
Results:
To address this issue, we formalize protein complexes as biclique spanned subgraphs, which include both sparse and dense subgraphs. We then cast the problem of protein complex prediction as a network partitioning into biclique spanned subgraphs with removal of minimum number of edges, called coherent partition. Since finding a coherent partition is a computationally intractable problem, we devise a parameter-free greedy approximation algorithm, termed Protein Complexes from Coherent Partition (PC2P), based on key properties of biclique spanned subgraphs. Through comparison with nine contenders, we demonstrate that PC2P: (i) successfully identifies modular structure in networks, as a prerequisite for protein complex prediction, (ii) outperforms the existing solutions with respect to a composite score of five performance measures on 75% and 100% of the analyzed PPI networks and gold standards in yeast and human, respectively, and (iii,iv) does not compromise GO semantic similarity and enrichment score of the predicted protein complexes. Therefore, our study demonstrates that clustering of networks in terms of biclique spanned subgraphs is a promising framework for detection of complexes in PPI networks.