Chung-Shou Liao

IsoRankN: spectral methods for global alignment of multiple protein networks

Motivation: With the increasing availability of large protein–protein interaction networks, the question of protein network alignment is becoming central to systems biology. Network alignment is further delineated into two sub-problems: local alignment, to find small conserved motifs across networks, and global alignment, which attempts to find a best mapping between all nodes of the two networks. In this article, our aim is to improve upon existing global alignment results. Better network alignment will enable, among other things, more accurate identification of functional orthologs across species. Results: We introduce IsoRankN (IsoRank-Nibble) a global multiple-network alignment tool based on spectral clustering on the induced graph of pairwise alignment scores. IsoRankN outperforms existing algorithms for global network alignment in coverage and consistency on multiple alignments of the five available eukaryotic networks. Being based on spectral methods, IsoRankN is both error tolerant and computationally efficient. Availability: Our software is available freely for non-commercial purposes on request from: http://isorank.csail.mit.edu/ Contact: bab@mit.edu

k -tuple domination in graphs

In a graph G, a vertex is said to dominate itself and all of its neighbors. For a fixed positive integer k, the k-tuple domination problem is to find a minimum sized vertex subset in a graph such that every vertex in the graph is dominated by at least k vertices in this set. The current paper studies k-tuple domination in graphs from an algorithmic point of view. In particular, we give a linear-time algorithm for the k-tuple domination problem in strongly chordal graphs, which is a subclass of chordal graphs and includes trees, block graphs, interval graphs and directed path graphs. We also prove that the k-tuple domination problem is NP-complete for split graphs (a subclass of chordal graphs) and for bipartite graphs.

IsoBase: a database of functionally related proteins across PPI networks

We describe IsoBase, a database identifying functionally related proteins, across five major eukaryotic model organisms: Saccharomyces cerevisiae, Drosophila melanogaster, Caenorhabditis elegans, Mus musculus and Homo Sapiens. Nearly all existing algorithms for orthology detection are based on sequence comparison. Although these have been successful in orthology prediction to some extent, we seek to go beyond these methods by the integration of sequence data and protein–protein interaction (PPI) networks to help in identifying true functionally related proteins. With that motivation, we introduce IsoBase, the first publicly available ortholog database that focuses on functionally related proteins. The groupings were computed using the IsoRankN algorithm that uses spectral methods to combine sequence and PPI data and produce clusters of functionally related proteins. These clusters compare favorably with those from existing approaches: proteins within an IsoBase cluster are more likely to share similar Gene Ontology (GO) annotation. A total of 48 120 proteins were clustered into 12 693 functionally related groups. The IsoBase database may be browsed for functionally related proteins across two or more species and may also be queried by accession numbers, species-specific identifiers, gene name or keyword. The database is freely available for download at http://isobase.csail.mit.edu/.

Power Domination Problem in Graphs

To monitor an electric power system by placing as few phase measurement units (PMUs) as possible is closely related to the famous vertex cover problem and domination problem in graph theory. A set S is a power dominating set (PDS) of a graph G=(V,E), if every vertex and every edge in the system is observed following the observation rules of power system monitoring. The minimum cardinality of a PDS of a graph G is the power domination number γp(G). We show that the problem of finding the power domination number for split graphs, a subclass of chordal graphs, is NP-complete. In addition, we present a linear time algorithm for finding γp(G) of an interval graph G, if the interval ordering of the graph is provided, and show that the algorithm with O(nlog n) time complexity, is asymptotically optimal, if the interval ordering is not given, where n is the number of intervals. We also show that the same results hold for the class of proper circular-arc graphs.

Capacitated Domination Problem

We consider a generalization of the well-known domination problem on graphs. The (soft) capacitated domination problem with demand constraints is to find a dominating set D of minimum cardinality satisfying both the capacity and demand constraints. The capacity constraint specifies that each vertex has a capacity that it can use to meet the demands of dominated vertices in its closed neighborhood, and the number of copies of each vertex allowed in D is unbounded. The demand constraint specifies the demand of each vertex in V to be met by the capacities of vertices in D dominating it. In this paper, we study the capacitated domination problem on trees from an algorithmic point of view. We present a linear time algorithm for the unsplittable demand model, and a pseudo-polynomial time algorithm for the splittable demand model. In addition, we show that the capacitated domination problem on trees with splittable demand constraints is NP-complete (even for its integer version) and provide a polynomial time approximation scheme (PTAS). We also give a primal-dual approximation algorithm for the weighted capacitated domination problem with splittable demand constraints on general graphs.

Power domination with bounded time constraints

Based on the power observation rules, the problem of monitoring a power utility network can be transformed into the graph-theoretic power domination problem, which is an extension of the well-known domination problem. A set

Power Domination in Circular-Arc Graphs

S

Reconstruction of phyletic trees by global alignment of multiple metabolic networks

S is a power dominating set (PDS) of a graph