Besides, a reachability query is also considered here as a related topic. Trivially, using this type of query, the original graph can be reconstructed. Many other operations, such as community finding, network pattern mining, and outlier detection, as well as common traversal mechanisms like Breadth-first search or Depth-first search, can be implemented based on neighborhood queries. Based on this query, it is desired to know all adjacent vertices of a given vertex. The interest of this paper is neighborhood query (as a general case of adjacency query). In general, a graph query is a computable function from a graph (or its representer) to a specific type, e.g., a Boolean value, a graph, or a relation. Also, contrary to bit compression techniques, this model is customized for a specific type of query with no need to decompress the whole graph.īoth model-based and forkable approaches focus on query analysis. Contrary to the model-based compression, the original graph can be fully reconstructed, if required, by forking all the data structure. Local decompression is the process of extracting the required information from just a specific part of the graph (e.g., adjacency list of a specific vertex). As an example, by extracting connected components and relabeling the vertices, one can rapidly state whether two desired vertices in the original graph are connected or not, without the ability to reconstruct the original graph.ģ) A specific type of compression technique, called here as forkable compression techniques, use special data structures such that an online local decompression is possible to answer desired queries. It might not be feasible to construct the original graph with these approaches. This group is not of interest in this paper.Ģ) Model-based compression approaches represent graphs by taking the advantages of special data structures, which are used for fast responding to pre-specified types of queries without any decompression. They are not often designed for specific processes on a graph and are introduced for less storage space and ease of transfer. Compression literature includes three major techniques:ġ) Bit compression methods, produce a compressed representation of the graph that should be decompressed in offline mode. However, according to some common aspects, related summarization approaches have also been discussed.Ĭompression approaches aim at finding a minimal data structure to store a graph. The proposed method of this paper is a compression technique. , ) from the input graph are removed to construct a sparse graph that preserves the desired attributes. those introduced in, , are divided into different categories including sparsification, which is more related to the topic of this paper. Summarization provides a smaller lossy description of a graph that may focus on some desired graph aspects. Several compression and summarization approaches have been introduced in the literature to achieve efficiency. However, working with big graphs is a challenging task. In recent years, graph representation has been frequently used as a structure for big-data storage to represent the links, friendships, similarities, distances, or any other relations. The results of applying the proposed method on toy and real datasets are compared with the state of the art that improves compression ratio and performance with an acceptable query response time. Then, this NP problem is approximated by a heuristic with a low degree polynomial time-complexity near to the complexity of the forward problem. This paper models an optimization problem to solve the inverse problem of finding the best compressed graph in order to minimize the reconstruction error. In other words, by traversing a compressed graph by depth of 2, from any desired vertex, its original adjacency list is reconstructed, with an acceptable error. The output of this method is a sparse graph optimized to keep original adjacent vertices, in at most 2-distance from each other and vice versa. The proposed approach, in this paper, is a lossy compression technique used to answer neighborhood queries with a more general precondition, called transitivity. Besides, their performance is usually a function of graph sparsity. These techniques mainly rely on local similarities of vertices. One successful category of them is based on local decompression designed to answer neighborhood queries. In recent years, many graph compression methods have been introduced.
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