Survey and Taxonomy of Lossless Graph Compression and Space-Efficient Graph Representations

Abstract

Various graphs such as web or social networks may contain up to trillions of edges. Compressing such datasets can accelerate graph processing by reducing the amount of I/O accesses and the pressure on the memory subsystem. Yet, selecting a proper compression method is challenging as there exist a plethora of techniques, algorithms, domains, and approaches in compressing graphs. To facilitate this, we present a survey and taxonomy on lossless graph compression that is the first, to the best of our knowledge, to exhaustively analyze this domain. Moreover, our survey does not only categorize existing schemes, but also explains key ideas, discusses formal underpinning in selected works, and describes the space of the existing compression schemes using three dimensions: areas of research (e.g., compressing web graphs), techniques (e.g., gap encoding), and features (e.g., whether or not a given scheme targets dynamic graphs). Our survey can be used as a guide to select the best lossless compression scheme in a given setting.

Towards Goal-Oriented Semantic Signal Processing: Applications and Future Challenges

“…As extensively studied in the literature, an adjacency matrix can be described by O(n 2 ) bits where n is the number of vertices. The number of required bits can be reduced to O(n log m + m log n) by using adjacency list representation, where m is the number of edges [170]. Since n and m can be reasonably small for practical scenarios, the resulting complexity becomes relatively low when the adjacency list representation is used.…”

“…Another line of research to compress the adjacency matrices includes universal codes for positive integers when the input probability distribution is not known as discussed in [170]. For instance, one may use Elias-γ codes to encode the elements of the adjacency matrix which require 2 log x + 1 bits to represent a positive integer x.…”

Slim Graph: Practical Lossy Graph Compression for Approximate Graph Processing, Storage, and Analytics

“…Most of the remaining schemes could be implemented as Slim Graph kernels. Second, lossless graph compression is summarized in a recent survey [24]; it is outside the Slim Graph scope. Third, many approximation graph algorithms have been develop to alleviate NP-Completeness and NP-Hardness of graph problems [49,55,55,66,76,90,158].…”

“…There exist many lossless schemes for graph compression, including WebGraph [33], k 2 -trees [37], and others [24]. They provide various degrees of storage reductions.…”

Parallel Algorithms for Finding Large Cliques in Sparse Graphs

“…The arboricity measures the number of such forests required for a given graph. Many real-world graphs are sparse [5,6,[9][10][11]14] and have a low degeneracy and arboricity [4,7,25,49,50].…”