Near Optimal Parallel Algorithms for Dynamic DFS in Undirected Graphs

Depth first search (DFS) tree is a fundamental data structure for solving graph problems. The classical algorithm [SiComp74] for building a DFS tree requires $O(m+n)$ time for a given graph $G$ having $n$ vertices and $m$ edges. Recently, Baswana et al. [SODA16] presented a simple algorithm for updating DFS tree of an undirected graph after an edge/vertex update in $\tilde{O}(n)$ time. However, their algorithm is strictly sequential. We present an algorithm achieving similar bounds, that can be adopted easily to the parallel environment. In the parallel model, a DFS tree can be computed from scratch using $m$ processors in expected $\tilde{O}(1)$ time [SiComp90] on an EREW PRAM, whereas the best deterministic algorithm takes $\tilde{O}(\sqrt{n})$ time [SiComp90,JAlg93] on a CRCW PRAM. Our algorithm can be used to develop optimal (upto polylog n factors deterministic algorithms for maintaining fully dynamic DFS and fault tolerant DFS, of an undirected graph. 1- Parallel Fully Dynamic DFS: Given an arbitrary online sequence of vertex/edge updates, we can maintain a DFS tree of an undirected graph in $\tilde{O}(1)$ time per update using $m$ processors on an EREW PRAM. 2- Parallel Fault tolerant DFS: An undirected graph can be preprocessed to build a data structure of size O(m) such that for a set of $k$ updates (where $k$ is constant) in the graph, the updated DFS tree can be computed in $\tilde{O}(1)$ time using $n$ processors on an EREW PRAM. Moreover, our fully dynamic DFS algorithm provides, in a seamless manner, nearly optimal (upto polylog n factors) algorithms for maintaining a DFS tree in semi-streaming model and a restricted distributed model. These are the first parallel, semi-streaming and distributed algorithms for maintaining a DFS tree in the dynamic setting.Comment: Accepted to appear in SPAA'17, 32 Pages, 5 Figure

Recent Advances in Fully Dynamic Graph Algorithms

In recent years, significant advances have been made in the design and analysis of fully dynamic algorithms. However, these theoretical results have received very little attention from the practical perspective. Few of the algorithms are implemented and tested on real datasets, and their practical potential is far from understood. Here, we present a quick reference guide to recent engineering and theory results in the area of fully dynamic graph algorithms

Efficient algorithms for analyzing large scale network dynamics: Centrality, community and predictability

Large scale networks are an indispensable part of our daily life; be it biological network, smart grids, academic collaboration networks, social networks, vehicular networks, or the networks as part of various smart environments, they are fast becoming ubiquitous. The successful realization of applications and services over them depend on efficient solution to their computational challenges that are compounded with network dynamics. The core challenges underlying large scale networks, for example: determining central (influential) nodes (and edges), interactions and contacts among nodes, are the basis behind the success of applications and services. Though at first glance these challenges seem to be trivial, the network characteristics affect their effective and efficient evaluation strategy. We thus propose to leverage large scale network structural characteristics and temporal dynamics in addressing these core conceptual challenges in this dissertation. We propose a divide and conquer based computationally efficient algorithm that leverages the underlying network community structure for deterministic computation of betweenness centrality indices for all nodes. As an integral part of it, we also propose a computationally efficient agglomerative hierarchical community detection algorithm. Next, we propose a network structure evolution based novel probabilistic link prediction algorithm that predicts set of links occurring over subsequent time periods with higher accuracy. To best capture the evolution process and have higher prediction accuracy we propose multiple time scales with the Markov prediction model. Finally, we propose to capture the multi-periodicity of human mobility pattern with sinusoidal intensity function of a cascaded nonhomogeneous Poisson process, to predict the future contacts over mobile networks. We use real data set and benchmarked approaches to validate the better performance of our proposed approaches --Abstract, page iii

Multilayer Graph-Based Trajectory Planning for Race Vehicles in Dynamic Scenarios

Trajectory planning at high velocities and at the handling limits is a challenging task. In order to cope with the requirements of a race scenario, we propose a far-sighted two step, multi-layered graph-based trajectory planner, capable to run with speeds up to 212~km/h. The planner is designed to generate an action set of multiple drivable trajectories, allowing an adjacent behavior planner to pick the most appropriate action for the global state in the scene. This method serves objectives such as race line tracking, following, stopping, overtaking and a velocity profile which enables a handling of the vehicle at the limit of friction. Thereby, it provides a high update rate, a far planning horizon and solutions to non-convex scenarios. The capabilities of the proposed method are demonstrated in simulation and on a real race vehicle.Comment: Accepted at The 22nd IEEE International Conference on Intelligent Transportation Systems, October 27 - 30, 201

Automated Functional Testing based on the Navigation of Web Applications

Web applications are becoming more and more complex. Testing such applications is an intricate hard and time-consuming activity. Therefore, testing is often poorly performed or skipped by practitioners. Test automation can help to avoid this situation. Hence, this paper presents a novel approach to perform automated software testing for web applications based on its navigation. On the one hand, web navigation is the process of traversing a web application using a browser. On the other hand, functional requirements are actions that an application must do. Therefore, the evaluation of the correct navigation of web applications results in the assessment of the specified functional requirements. The proposed method to perform the automation is done in four levels: test case generation, test data derivation, test case execution, and test case reporting. This method is driven by three kinds of inputs: i) UML models; ii) Selenium scripts; iii) XML files. We have implemented our approach in an open-source testing framework named Automatic Testing Platform. The validation of this work has been carried out by means of a case study, in which the target is a real invoice management system developed using a model-driven approach.Comment: In Proceedings WWV 2011, arXiv:1108.208