Abstract: Using a set of geometric containers to speed up shortest path queries in a weighted graph has been proven a useful tool for dealing with large sparse graphs. Given a layout of a graph G=(V,E), we store, for each edge (u,v)set membership, variantE, the bounding box of all nodes tset membership, variantV for which a shortest u-t-path starts with (u,v). Shortest path queries can then be answered by DijkstraImage restricted to edges where the corresponding bounding box contains the target.
In this paper, 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 bounding boxes have to be updated. We evaluate the quality and the time for different update strategies that guarantee correct shortestpaths in an interesting application to railway information systems, using real-world data from six European countries.
Abstract: Many efforts have been done in the last years to model public transport timetables in order to
find optimal routes. The proposed models can be classified into two types: those representing the
timetable as an array, and those representing it as a graph. The array-based models have been
shown to be very effective in terms of query time, while the graph-based models usually answer
queries by computing shortestpaths, and hence they are suitable to be used in combination with
speed-up techniques developed for road networks.
In this paper, we focus on the dynamic behavior of graph-based models considering the case
where transportation systems are subject to delays with respect to the given timetable. We
make three contributions: (i) we give a simplified and optimized update routine for the wellknown
time-expanded model along with an engineered query algorithm; (ii) we propose a new
graph-based model tailored for handling dynamic updates; (iii) we assess the effectiveness of
the proposed models and algorithms by an experimental study, which shows that both models
require negligible update time and a query time which is comparable to that required by some
array-based models.
Abstract: Dynamic graph algorithms have been extensively studied in the last two
decades due to their wide applicabilityin manycon texts. Recently, several
implementations and experimental studies have been conducted investigating
the practical merits of fundamental techniques and algorithms. In most
cases, these algorithms required sophisticated engineering and fine-tuning
to be turned into efficient implementations. In this paper, we surveysev -
eral implementations along with their experimental studies for dynamic
problems on undirected and directed graphs. The former case includes
dynamic connectivity, dynamic minimum spanning trees, and the sparsification
technique. The latter case includes dynamic transitive closure and
dynamic shortestpaths. We also discuss the design and implementation of
a software libraryfor dynamic graph algorithms.
Abstract: We describe algorithms for finding shortestpaths and distances in outerplanar and planar digraphs
that exploit the particular topology of the input graph. An important feature of our algorithms is that they can
work in a dynamic environment, where the cost of any edge can be changed or the edge can be deleted. In the
case of outerplanar digraphs, our data structures can be updated after any such change in only logarithmic time.
A distance query is also answered in logarithmic time. In the case of planar digraphs, we give an interesting
tradeoff between preprocessing, query, and update times depending on the value of a certain topological
parameter of the graph. Our results can be extended to n-vertex digraphs of genus O.n1¡"/ for any " > 0.
Abstract: We provide an improved FPTAS for multiobjective shortestpaths,a fundamental (NP_hard) problem in multiobjective optimization,along with a new generic method for obtaining FPTAS to any multiobjective optimization problem with non-linear objectives. We show how these results can be used to obtain better approximate solutions to three related problems that have important applications in QoS routing and in traffic optimization.
Abstract: We provide an improved FPTAS for multiobjective shortestpaths—a fundamental (NP-hard) problem in multiobjective optimization—along with a new generic method for obtaining FPTAS to any multiobjective optimization problem with non-linear objectives. We show how these results can be used to obtain better approximate solutions to three related problems, multiobjective constrained [optimal] path and non-additive shortest path, that have important applications in QoS routing and in traffic optimization. We also show how to obtain a FPTAS to a natural generalization of the weighted multicommodity flow problem with elastic demands and values that models several realistic scenarios in transportation and communication networks.
Abstract: This research attempts a first step towards investigating the aspect of radiation awareness in environments with abundant heterogeneous wireless networking. We call radiation at a point of a 3D wireless network the total amount of electromagnetic quantity the point is exposed to, our definition incorporates the effect of topology as well as the time domain, data traffic and environment aspects. Even if the impact of radiation to human health remains largely unexplored and controversial, we believe it is worth trying to understand and control. We first analyze radiation in well known topologies (random and grids), randomness is meant to capture not only node placement but also uncertainty of the wireless propagation model. This initial understanding of how radiation adds (over space and time) can be useful in network design, to reduce health risks. We then focus on the minimum radiation path problem of finding the lowest radiation trajectory of a person moving from a source to a destination point of the network region. We propose three heuristics which provide low radiation paths while keeping path length low, one heuristic gets in fact quite close to the offline solution we compute by a shortest path algorithm. Finally, we investigate the interesting impact on the heuristics' performance of diverse node mobility.
Abstract: In this work we consider temporal networks, i.e. networks defined by a labeling $\lambda$ assigning to each edge of an underlying graph G a set of discrete time-labels. The labels of an edge, which are natural numbers, indicate the discrete time moments at which the edge is available. We focus on path problems of temporal networks. In particular, we consider time-respecting paths, i.e. paths whose edges are assigned by $\lambda$ a strictly increasing sequence of labels. We begin by giving two efficient algorithms for computing shortest time-respecting paths on a temporal network. We then prove that there is a natural analogue of Menger’s theorem holding for arbitrary temporal networks. Finally, we propose two cost minimization parameters for temporal network design. One is the temporality of G, in which the goal is to minimize the maximum number of labels of an edge, and the other is the temporal cost of G, in which the goal is to minimize the total number of labels used. Optimization of these parameters is performed subject to some connectivity constraint. We prove several lower and upper bounds for the temporality and the temporal cost of some very basic graph families such as rings, directed acyclic graphs, and trees.
Abstract: The timetable information problem can be solved by computing shortestpaths in special graphs built from timetable data. In general, two models exist: the time-dependent and time-expanded network. In a recent work, both models are compared with respect to advantages and disadvantages on a theoretical and a practical framework. In addition, an extensive experimental evaluation reveals further differences with respect to query performance. However, delays which occur very frequently in railway systems are not covered. In this work, we show how the time-dependent and the time-expanded models should be updated in order to capture delays. It turns out that delays can be incorporated in the time-dependent model without changing the topology of the network. This is not true for the time-expanded model, whose updating involves a (sometimes large) sequence of edge insertions, deletions, and cost modifications.
Abstract: In many fields of application, shortest path finding problems
in very large graphs arise. Scenarios where large numbers of on-line
queries for shortestpaths have to be processed in real-time appear for example
in traffic information systems. In such systems, the techniques considered
to speed up the shortest path computation are usually based on
precomputed information. One approach proposed often in this context
is a space reduction, where precomputed shortestpaths are replaced by
single edges with weight equal to the length of the corresponding shortest
path. In this paper, we give a first systematic experimental study of
such a space reduction approach. We introduce the concept of multi-level
graph decomposition. For one specific application scenario from the field
of timetable information in public transport, we perform a detailed analysis
and experimental evaluation of shortest path computations based
on multi-level graph decomposition.
