Exact Vs. Approximated Diameter Calculation in Large Graphs

Abstract

A graph is a mathematical abstraction commonly used to represent relationships among a finite set of entities, such as hypertext documents or users in a social network. With the recent explosion of online content, the size and number of available graphs have increased as well, prompting research for efficient and scalable methods to process them in a timely fashion. This paper focuses on the calculation of the diameter of a graph, a well-known and relevant metric whose calculation poses a remarkable computational challenge for large graphs. We selected three algorithms based on two popular computing models: MapReduce and Bulk Synchronous Parallel (BSP). Two of the algorithms are based on MapReduce and calculate the exact and an approximated value for the graph diameter. The third algorithm is based on BSP and produces the exact value for the diameter. Our tests show that the approximated MapReduce solution produces the best combination of execution time and scalability, although it is outperformed in some cases by the exact BSP solution.