Min-Max Coverage in Multi-interface Networks

International audienceWe consider devices equipped with multiple wired or wireless interfaces. By switching among interfaces or by combining the available interfaces, each device might establish several connections. A connection is established when the devices at its endpoints share at least one active interface. Each interface is assumed to require an activation cost. In this paper, we consider the problem of establishing the connections defined by a network G = (V,E) while keeping as low as possible the maximum cost set of active interfaces at the single nodes. Nodes V represent the devices, edges E represent the connections that must be established. We study the problem of minimizing the maximum cost set of active interfaces among the nodes of the network in order to cover all the edges. We prove that the problem is NP-hard for any fixed Δ ≥ 5 and k ≥ 16, with Δ being the maximum degree, and k being the number of different interfaces among the network. We also show that the problem cannot be approximated within Ω(ln Δ). We then provide a general approximation algorithm which guarantees a factor of O((1 + b)ln (Δ)), with b being a parameter depending on the topology of the input graph. Interestingly, b can be bounded by a constant for many graph classes. Other approximation and exact algorithms for special cases are presented

Dynamic Shortest Path Algorithms for Hypergraphs

A hypergraph is a set V of vertices and a set of non-empty subsets of V, called hyperedges. Unlike graphs, hypergraphs can capture higher-order interactions in social and communication networks that go beyond a simple union of pairwise relationships. In this paper, we consider the shortest path problem in hypergraphs. We develop two algorithms for finding and maintaining the shortest hyperpaths in a dynamic network with both weight and topological changes. These two algorithms are the first to address the fully dynamic shortest path problem in a general hypergraph. They complement each other by partitioning the application space based on the nature of the change dynamics and the type of the hypergraph

Geometric shortest path containers [online]

In this paper, we consider Dijkstra\u27s algorithm for the single source single target shortest path problem in large sparse graphs. The goal is to reduce the response time for on-line queries by using precomputed information. Due to the size of the graph, preprocessing space requirements can be only linear in the number of nodes. We assume that a layout of the graph is given. In the preprocessing, we determine from this layout a geometric object for each edge containing all nodes that can be reached by a shortest path starting with that edge. Based on these geometric objects, the search space for on-line computation can be reduced significantly. Shortest path queries can then be answered by Dijkstra\u27s algorithm restricted to edges where the corresponding geometric object contains the target. We present an extensive experimental study comparing the impact of different types of objects. The test data we use are real-world traffic networks, the typical field of application for this scenario. Furthermore, we present new algorithms as well as an empirical study for the dynamic case of this problem, where edge weights are subject to change and the geometric containers have to be updated. We evaluate the quality and the time for different update strategies that guarantee correct shortest paths. Finally, we present a software framework in C++ to realize the implementations of all of our variants of Dijkstra\u27s algorithm. A basic implementation of the algorithm is refined for each modification and - even more importantly - these modifications can be combined in any possible way without loss of efficiency

Shortest path algorithms for dynamic transportation networks

Over the last decade, many interesting route planning problems can be solved by finding the shortest path in a weighted graph that represents a transportation network. Such networks are private transport networks or timetabled public transportation networks. In the shortest path problem, every network type requires different algorithms to compute one or more than one shortest path. However, routing in a public transportation network is completely different and is much more complex than routing in a private transport network, and therefore different algorithms are required. For large networks, the standard shortest path algorithms - Dijkstra's algorithm (1959) and Bellman's algorithm (1958)- are too slow. Consequently, faster algorithms have been designed to speed up the search. However, these algorithms often consider only the simplest scenario of finding an optimal route on a graph with static real edge costs. But real map routing problems are often not that simple – it is often necessary to consider time-dependent edge costs. For example, in public transportation routing, consideration of the time-dependent model of these networks is mandatory. However, there are a number of transportation applications that use informed search algorithms (where the algorithm uses heuristics that guide the search toward the destination), rather than one of the standard static shortest path algorithms. This is primarily due to shortest paths needing to be rapidly identified either because an immediate response is required. For example, the A* algorithm (Nilsson, 1971) is widely used in artificial intelligence. Heuristic information (in the form of estimated distance to the destination) is used to focus the search towards the destination node. This results in finding the shortest path faster than the standard static search algorithms. Road traffic congestion has become an increasingly significant problem in a modern society. In a dynamic traffic environment, traffic conditions are time-dependent. For instance, when travelling from home to the work, although an optimal route can be planned prior to departure based on the traffic conditions at that time, it may be necessary to adjust the route while en route because traffic conditions change all the time. In some cases, it is necessary to modify the travelling route from time to time and re-plan a new route from the current location to the destination, based on the real-time traffic information. The challenge lies in the fact that any modification to the optimal route to adapt to the dynamic environment necessitates speeding up of the search efforts. Among the algorithms suggested for the dynamic shortest path problem is the algorithm of Lifelong Planning A* algorithm (LPA*) (Koenig, Likhachev and Furcy, 2004). This algorithm has been given this name because of its ability to reuse information from previous searches. It is used to adjust a shortest path to adapt to the dynamic transportation network. Search space and fast shortest path queries can be used for finding fastest updated route on road and bus networks. Consequently, the efficient processing of both types of queries is of first-rate significance. However, most search methods focus only on one type of query and do not efficiently support the other. To address this challenge, this research presents the first novel approach; an Optimised Lifelong Planning A* (OLPA*) algorithm. The OLPA* used an appropriate data structure to improve the efficiency of the dynamic algorithms implementation making it capable of improving the search performance of the algorithm to solve the dynamic shortest path problem, which is where the traveller may have to re-compute the shortest path while travelling in a dynamic transportation environment. This research has also proposed bi-directional LPA* (BLPA*) algorithm. The proposed algorithm BLPA* used bi-directional search strategy and the main idea in this strategy is to divide the search problem into two separate problems. One search proceeds forwards from the start node, while the other search proceeds backwards from the end node. The solution requires the two search problems to meet at one middle node. The BLPA* algorithm has the same overall structure as the LPA* algorithm search, with some differences that the BLPA* contains a priority queue for each direction. This research presented another algorithm that designed to adaptively derive the shortest path to the desired destination by making use of previous search results and reducing the total execution time by using the benefits of a bi-directional search strategy . This novel algorithm has been called the bi-directional optimised Lifelong A* algorithm (BiOLPA*). It was originally proposed for road transport networks and later also applied to public transportation networks. For the road transport network, the experimental results demonstrate that the proposed incremental search approach considerably outperforms the original approach method, which recomputed the shortest path from scratch each time without utilization of the previous search results. However, for public transportation, the significant problem is that it is not possible to apply a bi-directional search backwards using estimated arrival time. This has been further investigated and a better understanding of why this technique fails has been documented. While the OLPA* algorithms give an impressive result when applied on bus network compared with original A* algorithms, and our experimental results demonstrate that the BiOLPA* algorithm on road network is significantly faster than the LPA*, OLPA* and the A* algorithms, not only in terms of number of expansion nodes but also in terms of computation time

Models and algorithms for the phone network cabling problem

Orientador: Arnaldo Vieira MouraDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de ComputaçãoResumo: O principal objetivo deste trabalho é a elaboração de heurísticas para auxiliar no projeto de cabeamento de redes telefônicas. O cabeamento será tratado desde os armários de distribuição até as caixas terminais. O auxílio de uma ferramenta computacional especializada no projeto de novas redes telefônicas abre caminhos para a minimização de custos e também reduz sensivelmente o tempo de planejamento. Inicialmente, estuda-se o problema para se obter uma especificação minuciosa, acompanhada de um modelo matemático. Com estas informações, desenvolve-se diferentes estratégias para algoritmos baseados na heurística GRASP, e compara-se os resultados experimentais obtidosAbstract: The main goal of these studies is the design of heuristics to support the planning of wire cabling on a phone network. The cabling will be handled from the central distribution point to terminal boxes. The assistance of a computational tool specialized in the design of phone networks raises new opportunities for cost reduction and decreases considerably the time spent designing the network. The problem is first studied in order to achieve a detailed specification with a mathematical model. Based on this information, several different strategies are laid out based on a heuristic called GRASP and the experimental results are compared.MestradoOtimização CombinatoriaMestre em Computaçã

Graph-based Analysis of Dynamic Systems

The analysis of dynamic systems provides insights into their time-dependent characteristics. This enables us to monitor, evaluate, and improve systems from various areas. They are often represented as graphs that model the system's components and their relations. The analysis of the resulting dynamic graphs yields great insights into the system's underlying structure, its characteristics, as well as properties of single components. The interpretation of these results can help us understand how a system works and how parameters influence its performance. This knowledge supports the design of new systems and the improvement of existing ones. The main issue in this scenario is the performance of analyzing the dynamic graph to obtain relevant properties. While various approaches have been developed to analyze dynamic graphs, it is not always clear which one performs best for the analysis of a specific graph. The runtime also depends on many other factors, including the size and topology of the graph, the frequency of changes, and the data structures used to represent the graph in memory. While the benefits and drawbacks of many data structures are well-known, their runtime is hard to predict when used for the representation of dynamic graphs. Hence, tools are required to benchmark and compare different algorithms for the computation of graph properties and data structures for the representation of dynamic graphs in memory. Based on deeper insights into their performance, new algorithms can be developed and efficient data structures can be selected. In this thesis, we present four contributions to tackle these problems: A benchmarking framework for dynamic graph analysis, novel algorithms for the efficient analysis of dynamic graphs, an approach for the parallelization of dynamic graph analysis, and a novel paradigm to select and adapt graph data structures. In addition, we present three use cases from the areas of social, computer, and biological networks to illustrate the great insights provided by their graph-based analysis. We present a new benchmarking framework for the analysis of dynamic graphs, the Dynamic Network Analyzer (DNA). It provides tools to benchmark and compare different algorithms for the analysis of dynamic graphs as well as the data structures used to represent them in memory. DNA supports the development of new algorithms and the automatic verification of their results. Its visualization component provides different ways to represent dynamic graphs and the results of their analysis. We introduce three new stream-based algorithms for the analysis of dynamic graphs. We evaluate their performance on synthetic as well as real-world dynamic graphs and compare their runtimes to snapshot-based algorithms. Our results show great performance gains for all three algorithms. The new stream-based algorithm StreaM_k, which counts the frequencies of k-vertex motifs, achieves speedups up to 19,043 x for synthetic and 2882 x for real-world datasets. We present a novel approach for the distributed processing of dynamic graphs, called parallel Dynamic Graph Analysis (pDNA). To analyze a dynamic graph, the work is distributed by a partitioner that creates subgraphs and assigns them to workers. They compute the properties of their respective subgraph using standard algorithms. Their results are used by the collator component to merge them to the properties of the original graph. We evaluate the performance of pDNA for the computation of five graph properties on two real-world dynamic graphs with up to 32 workers. Our approach achieves great speedups, especially for the analysis of complex graph measures. We introduce two novel approaches for the selection of efficient graph data structures. The compile-time approach estimates the workload of an analysis after an initial profiling phase and recommends efficient data structures based on benchmarking results. It achieves speedups of up to 5.4 x over baseline data structure configurations for the analysis of real-word dynamic graphs. The run-time approach monitors the workload during analysis and exchanges the graph representation if it finds a configuration that promises to be more efficient for the current workload. Compared to baseline configurations, it achieves speedups up to 7.3 x for the analysis of a synthetic workload. Our contributions provide novel approaches for the efficient analysis of dynamic graphs and tools to further investigate the trade-offs between different factors that influence the performance.:1 Introduction 2 Notation and Terminology 3 Related Work 4 DNA - Dynamic Network Analyzer 5 Algorithms 6 Parallel Dynamic Network Analysis 7 Selection of Efficient Graph Data Structures 8 Use Cases 9 Conclusion A DNA - Dynamic Network Analyzer B Algorithms C Selection of Efficient Graph Data Structures D Parallel Dynamic Network Analysis E Graph-based Intrusion Detection System F Molecular Dynamic