Abstract: We present a parallel priority queue that supports the following operations in
constant time: parallel insertion of a sequence of elements ordered according
to key, parallel decrease key for a sequence of elements ordered according to
key, deletion of the minimum key element, and deletion of an arbitrary element.
Our data structure is the first to support multi-insertion and multi-decrease key in
constant time. The priority queue can be implemented on the EREW PRAM and
can perform any sequence of n operations in O(n) time and O(m log n) work, m
being the total number of keyes inserted and/or updated. A main application is a
parallel implementation of Dijkstra¢s algorithm for the single-source shortestpath
problem, which runs in O(n) time and O(m log n) work on a CREW PRAM on
graphs with n vertices and m edges. This is a logarithmic factor improvement in
the running time compared with previous approaches.
Abstract: We present a simple parallel algorithm for the single-source shortestpath
problem in planar digraphs with nonnegative real edge weights. The algorithm runs
on the EREW PRAM model of parallel computation in O((n2=+n1&=) log n)
time, performing O(n1+= log n) work for any 0<{\aa}<1/2. The strength of the
algorithm is its simplicity, making it easy to implement and presumable quite
efficient in practice. The algorithm improves upon the work of all previous
parallel algorithms. Our algorithm is based on a region decomposition of the
input graph and uses a well-known parallel implementation of Dijkstra's
algorithm. The logarithmic factor in both the work and the time can be
eliminated by plugging in a less practical, sequential planar shortestpath
algorithm together with an improved parallel implementation of Dijkstra's
algorithm.
Abstract: Using a set of geometric containers to speed up shortestpath 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). Shortestpath 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: We consider two approaches that model timetable information in public transportation systems
as shortest-path problems in weighted graphs. In the time-expanded approach, every event at
a station, e.g., the departure of a train, is modeled as a node in the graph, while in the timedependent
approach the graph contains only one node per station. Both approaches have been
recently considered for (a simplified version of) the earliest arrival problem, but little is known
about their relative performance. Thus far, there are only theoretical arguments in favor of the
time-dependent approach. In this paper, we provide the first extensive experimental comparison of
the two approaches. Using several real-world data sets, we evaluate the performance of the basic
models and of several new extensions towards realistic modeling. Furthermore, new insights on
solving bicriteria optimization problems in both models are presented. The time-expanded approach
turns out to be more robust for modeling more complex scenarios, whereas the time-dependent
approach shows a clearly better performance.
Abstract: We consider two approaches that model timetable information in public transportation systems
as shortest-path problems in weighted graphs. In the time-expanded approach, every event at
a station, e.g., the departure of a train, is modeled as a node in the graph, while in the timedependent
approach the graph contains only one node per station. Both approaches have been
recently considered for (a simplified version of) the earliest arrival problem, but little is known
about their relative performance. Thus far, there are only theoretical arguments in favor of the
time-dependent approach. In this paper, we provide the first extensive experimental comparison of
the two approaches. Using several real-world data sets, we evaluate the performance of the basic
models and of several new extensions towards realistic modeling. Furthermore, new insights on
solving bicriteria optimization problems in both models are presented. The time-expanded approach
turns out to be more robust for modeling more complex scenarios, whereas the time-dependent
approach shows a clearly better performance.
Abstract: One of the most important applications of wireless sensor
networks is building monitoring and more speci cally, the
early detection of emergency events and the provision of
guidance for safe evacuation of the building. In this pa-
per, we describe a demo application that, in the event of a
re inside a monitored building, uses the information from
the deployed sensor network in order to nd the shortest
safest path away from the emergency and provides naviga-
tion guidance to the occupants (modelled by a mobile robot),
in order to safely evacuate the building. For this demo, we
developed our own ad-hoc robot-sensor interconnection us-
ing expansion connectors and programming in a low-level
language.
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: A fundamental approach in finding efficiently best routes or optimal itineraries in traffic information
systems is to reduce the search space (part of graph visited) of the most commonly used
shortestpath routine (Dijkstra¢s algorithm) on a suitably defined graph. We investigate reduction
of the search space while simultaneously retaining data structures, created during a preprocessing
phase, of size linear (i.e., optimal) to the size of the graph. We show that the search space of
Dijkstra¢s algorithm can be significantly reduced by extracting geometric information from a given
layout of the graph and by encapsulating precomputed shortest-path information in resulted geometric
objects (containers). We present an extensive experimental study comparing the impact of
different types of geometric containers using test data from real-world traffic networks. We also
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 and show that
our new methods are two to three times faster than recomputing everything from scratch. Finally,
in an appendix, we discuss the software framework that we developed to realize the implementations
of all of our variants of Dijkstra¢s algorithm. Such a framework is not trivial to achieve as our
goal was to maintain a common code base that is, at the same time, small, efficient, and flexible,
as we wanted to enhance and combine several variants in any possible way.
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 shortestpath, 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: The non-additive shortestpath (NASP) problem asks for
finding an optimal path that minimizes a certain multi-attribute nonlinear
cost function. In this paper, we consider the case of a non-linear
convex and non-decreasing function on two attributes.We present an efficient
polynomial algorithm for solving a Lagrangian relaxation of NASP.
We also present an exact algorithm that is based on new heuristics we
introduce here, and conduct a comparative experimental study with synthetic
and real-world data that demonstrates the quality of our approach.
Abstract: Understanding the graph structure of the Internet is a crucial step for building accurate
network models and designing efficient algorithms for Internet applications.Yet,obtaining this graph
structure can be a surprisingly difficult task,as edges cannot be explicitly queried.For instance,
empirical studies of the network of InternetProtocol (IP) addresses typically rely on indirect methods
like trace route to build what are approximately single-source,all-destinations,shortest-path trees.
These trees only sample a fraction of the network’s edges,and a paper by Lakhinaetal.[2003]found
empirically that there sulting sample is intrinsically biased.Further,in simulations,they observed that the degree distribution under trace route sampling exhibits a power law even when the underlying
degree distribution is Poisson.
Abstract: We investigate the practical merits of a parallel priority queue
through its use in the development of a fast and work-efficient parallel
shortestpath algorithm, originally designed for an EREW PRAM. Our
study reveals that an efficient implementation on a real supercomputer
requires considerable effort to reduce the communication performance
(which in theory is assumed to take constant time). It turns out that the
most crucial part of the implementation is the mapping of the logical
processors to the physical processing nodes of the supercomputer. We
achieve the requested efficient mapping through a new graph-theoretic
result of independent interest: computing a Hamiltonian cycle on a directed
hyper-torus. No such algorithm was known before for the case of
directed hypertori. Our Hamiltonian cycle algorithm allows us to considerably
improve the communication cost and thus the overall performance
of our implementation.
Abstract: We study network connection games where the nodes of a networ
k perform edge swaps
in order to improve their communication costs. For the model
proposed by [2], in which the selfish
cost of a node is the sum of all shortestpath distances to the o
ther nodes, we use the probabilistic
method to provide a new, structural characterization of equ
ilibrium graphs. We show how to use this
characterization in order to prove upper bounds on the diame
ter of equilibrium graphs in terms of the
size of the largest
k
-vicinity (defined as the the set of vertices within distance
k
from a vertex), for
any
k
≥
1 and in terms of the number of edges, thus settling positivel
y a conjecture of [2] in the cases
of graphs of large
k
-vicinity size (including graphs of large maximum degree) a
nd of graphs which are
dense enough.
Next, we present a new swap-based network creation game, in w
hich selfish costs depend on the imme-
diate neighborhood of each node; in particular, the profit of
a node is defined as the sum of the degrees
of its neighbors. We prove that, in contrast to the previous m
odel, this network creation game admits
an exact potential, and also that any equilibrium graph cont
ains an induced star. The existence of the
potential function is exploited in order to show that an equi
librium can be reached in expected polyno-
mial time even in the case where nodes can only acquire limite
d knowledge concerning non-neighboring
nodes.
Abstract: In this work, we study the impact of dynamically changing link capacities on the delay bounds of LIS (Longest-In-System) and SIS (Shortest-In-System) protocols on specific networks (that can be modelled as Directed Acyclic Graphs (DAGs)) and stability bounds of greedy contention–resolution protocols running on arbitrary networks under the Adversarial Queueing Theory. Especially, we consider the model of dynamic capacities, where each link capacity may take on integer values from [1,C] with C>1, under a (w,\~{n})-adversary. We show that the packet delay on DAGs for LIS is upper bounded by O(iw\~{n}C) and lower bounded by {\`U}(iw\~{n}C) where i is the level of a node in a DAG (the length of the longest path leading to node v when nodes are ordered by the topological order induced by the graph). In a similar way, we show that the performance of SIS on DAGs is lower bounded by {\`U}(iw\~{n}C), while the existence of a polynomial upper bound for packet delay on DAGs when SIS is used for contention–resolution remains an open problem. We prove that every queueing network running a greedy contention–resolution protocol is stable for a rate not exceeding a particular stability threshold, depending on C and the length of the longest path in the network.
Abstract: We consider the QoS-aware Multicommodity Flow problem,
a natural generalization of the weighted multicommodity flow problem
where the demands and commodity values are elastic to the Quality-of-
Service characteristics of the underlying network. The problem is fundamental
in transportation planning and also has important applications
beyond the transportation domain. We provide a FPTAS for the QoSaware
Multicommodity Flow problem by building upon a Lagrangian
relaxation method and a recent FPTAS for the non-additive shortestpath problem.
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 shortestpath algorithm. Finally, we investigate the interesting impact on the heuristics' performance of diverse node mobility.
Abstract: We consider the problem of preprocessing an n-vertex digraph with real edge weights so that
subsequent queries for the shortestpath or distance between any two vertices can be efficiently answered. We
give algorithms that depend on the treewidth of the input graph. When the treewidth is a constant, our algorithms
can answer distance queries in O ({\'a}(n) ) time after O.n/ preprocessing. This improves upon previously known
results for the same problem.We also give a dynamic algorithm which, after a change in an edge weight, updates
the data structure in time O.n¯ /, for any constant 0 < ¯ < 1. Furthermore, an algorithm of independent interest
is given: computing a shortestpath tree, or finding a negative cycle in linear time.
Abstract: We consider the problem of preprocessing an n-vertex digraph with real edge weights so that subsequent queries for the shortestpath or distance between any two vertices can be efficiently answered. We give parallel algorithms for the EREW PRAM model of computation that depend on the treewidth of the input graph. When the treewidth is a constant, our algorithms can answer distance queries in O({\'a}(n)) time using a single processor, after a preprocessing of O(log2n) time and O(n) work, where {\'a}(n) is the inverse of Ackermann's function. The class of constant treewidth graphs contains outerplanar graphs and series-parallel graphs, among others. To the best of our knowledge, these are the first parallel algorithms which achieve these bounds for any class of graphs except trees. We also give a dynamic algorithm which, after a change in an edge weight, updates our data structures in O(log n) time using O(n{\^a}) work, for any constant 0 < {\^a} < 1. Moreover, we give an algorithm of independent interest: computing a shortestpath tree, or finding a negative cycle in O(log2n) time using O(n) work.
Abstract: We study computational and coordination efficiency issues of
Nash equilibria in symmetric network congestion games. We first propose
a simple and natural greedy method that computes a pure Nash equilibrium
with respect to traffic congestion in a network. In this algorithm
each user plays only once and allocates her traffic to a path selected via
a shortestpath computation. We then show that this algorithm works
for series-parallel networks when users are identical or when users are of
varying demands but have the same best response strategy for any initial
network traffic. We also give constructions where the algorithm fails if
either the above condition is violated (even for series-parallel networks)
or the network is not series-parallel (even for identical users). Thus, we
essentially indicate the limits of the applicability of this greedy approach.
We also study the price of anarchy for the objective of maximum
latency. We prove that for any network of m uniformly related links and
for identical users, the price of anarchy is {\`E}( logm
log logm).
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: We give an overview of models and efficient algorithms for
optimally solving timetable information problems like “given a departure
and an arrival station as well as a departure time, which is the
connection that arrives as early as possible at the arrival station?” Two
main approaches that transform the problems into shortestpath problems
are reviewed, including issues like the modeling of realistic details
(e.g., train transfers) and further optimization criteria (e.g., the number
of transfers). An important topic is also multi-criteria optimization,
where in general all attractive connections with respect to several criteria
shall be determined. Finally, we discuss the performance of the described
algorithms, which is crucial for their application in a real system.
Abstract: We give an overview of models and efficient algorithms for optimally solving timetable information problems like “given a departure and an arrival station as well as a departure time, which is the connection that arrives as early as possible at the arrival station?” Two main approaches that transform the problems into shortestpath problems are reviewed, including issues like the modeling of realistic details (e.g., train transfers) and further optimization criteria (e.g., the number of transfers). An important topic is also multi-criteria optimization, where in general all attractive connections with respect to several criteria shall be determined. Finally, we discuss the performance of the described algorithms, which is crucial for their application in a real system.
Abstract: In many fields of application, shortestpath 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 shortestpath 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 shortestpath. 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 shortestpath computations based
on multi-level graph decomposition.
