77,641 research outputs found
Solving Assignment and Routing Problems in Mixed Traffic Systems
This doctoral thesis presents not only a new traffic assignment model for mixed traffic systems but also new heuristics for multi-paths routing problems, a case study in Hanoi Vietnam, and a new software, named TranOpt Plus, supporting three major features: map editing, dynamic routing, and traffic assignment modeling.
We investigate three routing problems: k shortest loop-less paths (KSLP), dissimilar shortest loop-less paths (DSLP), and multi-objective shortest paths (MOSP). By developing loop filters and a similarity filter, we create two new heuristics based on Eppstein's algorithm: one using loop filters for the KSLP problem (HELF), the other using loop-and-similarity filters for the DSLP problem (HELSF). The computational results on real street maps indicate that the new heuristics dominate the other algorithms considered in terms of either running time or the average length of the found paths.
In traffic assignment modeling, we propose a new User Equilibrium (UE) model, named GUEM, for mixed traffic systems where 2- and 4-wheel vehicles travel together without any separate lanes for each kind of vehicle. At the optimal solution to the model, a user equilibrium for each kind of vehicle is obtained. The model is applied to the traffic system in Hanoi, Vietnam, where the traffic system is mixed traffic dominated by motorcycles. The predicted assignment by the GUEM model using real collected data in Hanoi is in high agreement with the real traffic situation in Hanoi.
Finally, we present the TranOpt Plus software, containing the implementation of all the routing algorithms mentioned in the thesis, as well as the GUEM model and a number of popular traffic assignment models for both standard traffic systems and mixed traffic systems. With its intuitive graphical user interface (GUI) and its strong visualization tools, TranOpt Plus also enables users without any mathematical or computer science background to use conveniently. Nevertheless, TranOpt Plus can be easily extended by further map-related problems, e.g., transportation network design, facility location, and the traveling salesman problem.
Keywords: mixed traffic assignment modeling, routing algorithms, shortest paths, dissimilar paths, Hanoi, TranOpt Plus, map visualizatio
Shortest path embeddings of graphs on surfaces
The classical theorem of F\'{a}ry states that every planar graph can be
represented by an embedding in which every edge is represented by a straight
line segment. We consider generalizations of F\'{a}ry's theorem to surfaces
equipped with Riemannian metrics. In this setting, we require that every edge
is drawn as a shortest path between its two endpoints and we call an embedding
with this property a shortest path embedding. The main question addressed in
this paper is whether given a closed surface S, there exists a Riemannian
metric for which every topologically embeddable graph admits a shortest path
embedding. This question is also motivated by various problems regarding
crossing numbers on surfaces.
We observe that the round metrics on the sphere and the projective plane have
this property. We provide flat metrics on the torus and the Klein bottle which
also have this property.
Then we show that for the unit square flat metric on the Klein bottle there
exists a graph without shortest path embeddings. We show, moreover, that for
large g, there exist graphs G embeddable into the orientable surface of genus
g, such that with large probability a random hyperbolic metric does not admit a
shortest path embedding of G, where the probability measure is proportional to
the Weil-Petersson volume on moduli space.
Finally, we construct a hyperbolic metric on every orientable surface S of
genus g, such that every graph embeddable into S can be embedded so that every
edge is a concatenation of at most O(g) shortest paths.Comment: 22 pages, 11 figures: Version 3 is updated after comments of
reviewer
MAP: Medial Axis Based Geometric Routing in Sensor Networks
One of the challenging tasks in the deployment of dense wireless networks (like sensor networks) is in devising a routing scheme for node to node communication. Important consideration includes scalability, routing complexity, the length of the communication paths and the load sharing of the routes. In this paper, we show that a compact and expressive abstraction of network connectivity by the medial axis enables efficient and localized routing. We propose MAP, a Medial Axis based naming and routing Protocol that does not require locations, makes routing decisions locally, and achieves good load balancing. In its preprocessing phase, MAP constructs the medial axis of the sensor field, defined as the set of nodes with at least two closest boundary nodes. The medial axis of the network captures both the complex geometry and non-trivial topology of the sensor field. It can be represented compactly by a graph whose size is comparable with the complexity of the geometric features (e.g., the number of holes). Each node is then given a name related to its position with respect to the medial axis. The routing scheme is derived through local decisions based on the names of the source and destination nodes and guarantees delivery with reasonable and natural routes. We show by both theoretical analysis and simulations that our medial axis based geometric routing scheme is scalable, produces short routes, achieves excellent load balancing, and is very robust to variations in the network model
Metric combinatorics of convex polyhedra: cut loci and nonoverlapping unfoldings
This paper is a study of the interaction between the combinatorics of
boundaries of convex polytopes in arbitrary dimension and their metric
geometry.
Let S be the boundary of a convex polytope of dimension d+1, or more
generally let S be a `convex polyhedral pseudomanifold'. We prove that S has a
polyhedral nonoverlapping unfolding into R^d, so the metric space S is obtained
from a closed (usually nonconvex) polyhedral ball in R^d by identifying pairs
of boundary faces isometrically. Our existence proof exploits geodesic flow
away from a source point v in S, which is the exponential map to S from the
tangent space at v. We characterize the `cut locus' (the closure of the set of
points in S with more than one shortest path to v) as a polyhedral complex in
terms of Voronoi diagrams on facets. Analyzing infinitesimal expansion of the
wavefront consisting of points at constant distance from v on S produces an
algorithmic method for constructing Voronoi diagrams in each facet, and hence
the unfolding of S. The algorithm, for which we provide pseudocode, solves the
discrete geodesic problem. Its main construction generalizes the source
unfolding for boundaries of 3-polytopes into R^2. We present conjectures
concerning the number of shortest paths on the boundaries of convex polyhedra,
and concerning continuous unfolding of convex polyhedra. We also comment on the
intrinsic non-polynomial complexity of nonconvex polyhedral manifolds.Comment: 47 pages; 21 PostScript (.eps) figures, most in colo
The Shortest Path to Happiness: Recommending Beautiful, Quiet, and Happy Routes in the City
When providing directions to a place, web and mobile mapping services are all
able to suggest the shortest route. The goal of this work is to automatically
suggest routes that are not only short but also emotionally pleasant. To
quantify the extent to which urban locations are pleasant, we use data from a
crowd-sourcing platform that shows two street scenes in London (out of
hundreds), and a user votes on which one looks more beautiful, quiet, and
happy. We consider votes from more than 3.3K individuals and translate them
into quantitative measures of location perceptions. We arrange those locations
into a graph upon which we learn pleasant routes. Based on a quantitative
validation, we find that, compared to the shortest routes, the recommended ones
add just a few extra walking minutes and are indeed perceived to be more
beautiful, quiet, and happy. To test the generality of our approach, we
consider Flickr metadata of more than 3.7M pictures in London and 1.3M in
Boston, compute proxies for the crowdsourced beauty dimension (the one for
which we have collected the most votes), and evaluate those proxies with 30
participants in London and 54 in Boston. These participants have not only rated
our recommendations but have also carefully motivated their choices, providing
insights for future work.Comment: 11 pages, 7 figures, Proceedings of ACM Hypertext 201
An evaluation of best compromise search in graphs
This work evaluates two different approaches for multicriteria graph
search problems using compromise preferences. This approach focuses search on
a single solution that represents a balanced tradeoff between objectives, rather
than on the whole set of Pareto optimal solutions. We review the main concepts
underlying compromise preferences, and two main approaches proposed for their
solution in heuristic graph problems: naive Pareto search (NAMOA
), and a k-shortest-path approach (kA
). The performance of both approaches is evaluated
on sets of standard bicriterion road map problems. The experiments reveal that
the k-shortest-path approach looses effectiveness in favor of naive Pareto search
as graph size increases. The reasons for this behavior are analyzed and discussedPartially funded by P07-TIC-03018, Cons. Innovación, Ciencia y
Empresa (Junta Andalucía), and Univ. Málaga, Campus Excel. Int. Andalucía Tec
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