You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
Integrating data from heterogeneous sources is often modeled as merging graphs. Given two or more 'compatible', but not-isomorphic graphs, the first step is to identify a graph alignment, where a potentially partial mapping of vertices between two graphs is computed. A significant portion of the literature on this problem only takes the global structure of the input graphs into account. Only more recent ones additionally use vertex and edge attributes to achieve a more accurate alignment. However, these methods are not designed to scale to map large graphs arising in many modern applications. We propose a new iterative graph aligner, gsaNA, that uses the global structure of the graphs to significantly reduce the problem size and align large graphs with a minimal loss of information. Concretely, we show that our proposed technique is highly flexible, can be used to achieve higher recall, and it is orders of magnitudes faster than the current state of the art techniques.

Cited Abstract(s):
[1]: We describe an algorithm, IsoRank, for global alignment of two protein-protein interaction (PPI) networks. IsoRank aims to maximize the overall match between the two networks; in contrast, much of previous work has focused on the local alignment problem-- identifying many possible alignments, each corresponding to a local region of similarity. IsoRank is guided by the intuition that a protein should be matched with a protein in the other network if and only if the neighbors of the two proteins can also be well matched. We encode this intuition as an eigenvalue problem, in a manner analogous to Google's PageRank method. We use IsoRank to compute the first known global alignment between the S. cerevisiae and D. melanogaster PPI networks. The common subgraph has 1420 edges and describes conserved functional components between the two species. Comparisons of our results with those of a well-known algorithm for local network alignment indicate that the globally optimized alignment resolves ambiguity introduced by multiple local alignments. Finally, we interpret the results of global alignment to identify functional orthologs between yeast and fly; our functional ortholog prediction method is much simpler than a recently proposed approach and yet provides results that are more comprehensive.

[2]: 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 multiplenetwork 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
As an example of spectral methods, IsoRank [1] ---one of the earliest global alignment work in computational biology---suggests an eigenvalue problem that approximates the objective of finding the maximum common subgraph. After finding the vertex similarity matrix, IsoRank finds the alignment by solving the maximum weighted bipartite matching. IsoRank finds a 1 2-approximate matching using a greedy method, which aligns pair of vertices in the order of highest estimated similarity. IsoRank was extended to multiple networks in [2] , where pairwise similarity matrices are computed and an iterative spectral clustering is used to output set of vertices, one from each network, that aligns with each other. It is noted that it cannot handle more than five networks.