Graph is a fundamental data structure that captures relationships between different data entities. In practice, graphs are widely used for modeling complicated data in different application domains such as social networks, protein networks, transportation networks, bibliographical networks, knowledge bases and many more. Currently, graphs with millions and billions of nodes and edges have become very common. In principle, graph analytics is an important big data discovery technique. Therefore, with the increasing abundance of large graphs, designing scalable systems for processing and analyzing large scale graphs has become one of the most timely problems facing the big data research community. In general, scalable processing of big graphs is B Sherif Sakr a challenging task due to their size and the inherent irregular structure of graph computations. Thus, in recent years, we have witnessed an unprecedented interest in building big graph processing systems that attempted to tackle these challenges. In this article, we provide a comprehensive survey over the state-of-the-art of large scale graph processing platforms. In addition, we present an extensive experimental study of five popular systems in this domain, namely, GraphChi, Apache Giraph, GPS, GraphLab and GraphX. In particular, we report and analyze the performance characteristics of these systems using five common graph processing algorithms and seven large graph datasets. Finally, we identify a set of the current open research challenges and discuss some promising directions for future research in the domain of large scale graph processing.

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Abstract. This paper considers the problem of finding a quickest path between two points in the Euclidean plane in the presence of a transportation network. A transportation network consists of a planar network where each road (edge) has an individual speed. A traveller may enter and exit the network at any point on the roads. Along any road the traveller moves with a fixed speed depending on the road, and outside the network the traveller moves at unit speed in any direction. We give an exact algorithm for the basic version of the problem: given a transportation network of total complexity n in the Euclidean plane, a source point s and a destination point t, find a quickest path between s and t. We also show how the transportation network can be preprocessed in time O(n 2 log n) into a data structure of size O(n 2 ) such that a (1 + ε)-approximate quickest path cost queries between any two points in the plane can be answered in time O(1/ε 4 log n).

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