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.
In a more recent work, propose Final @cite_12 to solve attributed network alignment problem. Final extends the concept of IsoRank @cite_16 , and make it capable to benefit from attribute information of the vertices and edges to solve this problem. In addition to graph's vertex, edge and attribute sets Final adds an optional input called prior knowledge matrix (H) in which each entry gives likelihood to align two vertices. Final is one of the most recent works which solves attributed graph alignment problem and outperforms @cite_16 @cite_22 @cite_31 @cite_8 .
@cite_22 @cite_8 @cite_31 @cite_16 @cite_12
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Knowledge graphs contain knowledge about the world and provide a structured representation of this knowledge. Current knowledge graphs contain only a small subset of what is true in the world. Link prediction approaches aim at predicting new links for a knowledge graph given the existing links between the entities. Tensor factorization approaches have proved promising for such link prediction problems. Proposed in 1927, Canonical Polyadic (CP) decomposition is among the first tensor factorization approaches. CP generally performs poorly for link prediction as it learns two independent embedding vectors for each entity, whereas they are really tied. We present a simple enhancement (which we call SimplE) of CP to allow the two embeddings of each entity to be learned dependently. The complexity of SimplE grows linearly with the size of embeddings. The embeddings learned through SimplE are interpretable, and certain types of background knowledge in terms of logical rules can be incorporated into these embeddings through weight tying. We prove SimplE is fully-expressive and derive a bound on the size of its embeddings for full expressivity. We show empirically that, despite its simplicity, SimplE outperforms several state-of-the-art tensor factorization techniques. Multiple networks naturally appear in numerous high-impact applications. Network alignment (i.e., finding the node correspondence across different networks) is often the very first step for many data mining tasks. Most, if not all, of the existing alignment methods are solely based on the topology of the underlying networks. Nonetheless, many real networks often have rich attribute information on nodes and or edges. In this paper, we propose a family of algorithms FINAL to align attributed networks. The key idea is to leverage the node edge attribute information to guide (topology-based) alignment process. We formulate this problem from an optimization perspective based on the alignment consistency principle, and develop effective and scalable algorithms to solve it. Our experiments on real networks show that (1) by leveraging the attribute information, our algorithms can significantly improve the alignment accuracy (i.e., up to a 30 improvement over the existing methods); (2) compared with the exact solution, our proposed fast alignment algorithm leads to a more than 10 times speed-up, while preserving a 95 accuracy; and (3) our on-query alignment method scales linearly, with an around 90 ranking accuracy compared with our exact full alignment method and a near real-time response time. In the study of deterministic distributed algorithms it is commonly assumed that each node has a unique O(log n)-bit identifier. We prove that for a general class of graph problems, local algorithms (constant-time distributed algorithms) do not need such identifiers: a port numbering and orientation is sufficient. Our result holds for so-called simple PO-checkable graph optimisation problems; this includes many classical packing and covering problems such as vertex covers, edge covers, matchings, independent sets, dominating sets, and edge dominating sets. We focus on the case of bounded-degree graphs and show that if a local algorithm finds a constant-factor approximation of a simple PO-checkable graph problem with the help of unique identifiers, then the same approximation ratio can be achieved on anonymous networks. As a corollary of our result and by prior work, we derive a tight lower bound on the local approximability of the minimum edge dominating set problem. Our main technical tool is an algebraic construction of homogeneously ordered graphs: We say that a graph is (α,r)-homogeneous if its nodes are linearly ordered so that an α fraction of nodes have pairwise isomorphic radius-r neighbourhoods. We show that there exists a finite (α,r)-homogeneous 2k-regular graph of girth at least g for any α We introduce a fully online model of maximum cardinality matching in which all vertices arrive online. On the arrival of a vertex, its incident edges to previously-arrived vertices are revealed. Each vertex has a deadline that is after all its neighbors’ arrivals. If a vertex remains unmatched until its deadline, the algorithm must then irrevocably either match it to an unmatched neighbor, or leave it unmatched. The model generalizes the existing one-sided online model and is motivated by applications including ride-sharing platforms, real-estate agency, etc. We show that the Ranking algorithm by (STOC 1990) is 0.5211-competitive in our fully online model for general graphs. Our analysis brings a novel charging mechanic into the randomized primal dual technique by (SODA 2013), allowing a vertex other than the two endpoints of a matched edge to share the gain. To our knowledge, this is the first analysis of Ranking that beats 0.5 on general graphs in an online matching problem, a first step towards solving the open problem by (STOC 1990) about the optimality of Ranking on general graphs. If the graph is bipartite, we show that the competitive ratio of Ranking is between 0.5541 and 0.5671. Finally, we prove that the fully online model is strictly harder than the previous model as no online algorithm can be 0.6317