Hugo A. D. do Nascimento

Automatic visualisation of metro maps

We investigate the new problem of automatic metro map layout. In general, a metro map consists of a set of lines which have intersections or overlaps. We define a set of aesthetic criteria for good metro map layouts and present a method to produce such layouts automatically. Our method uses a variation of the spring algorithm with a suitable preprocessing step. The experimental results with real world data sets show that our method produces good metro map layouts quickly.

User Hints for map labeling

Cartography is one of the oldest forms of visualization. It has applications not only in geography but in many other science fields. A significant visual problem in cartography is the map-labeling problem, which consists of assigning positions for the labels of graphical features of a map so that these elements can be uniquely identified. Although much research has been done on map labeling, practical labeling processes still demand intensive manual work to produce high-quality solutions. One reasons for this is that the optimization problems associated with map labeling are NP-hard. More importantly, existing automatic labeling methods do not incorporate all kinds of domain knowledge that may be of interest for a cartographer. In the present paper, we describe an interactive framework for assisting cartographers in the map-labeling problem. We treat labeling processes as an optimization task, and support human interaction combined with fully automatic methods in a general framework that we call User Hints. An interactive map-labeling system based on the User Hints framework is presented, and an evaluation of such system with real experts in cartography is described. This evaluation shows that our interactive map-labeling framework is promising.

User hints: a framework for interactive optimization

Innovative improvements in the area of human-computer interaction and user interfaces have enabled intuitive and effective applications for a variety of problems. On the other hand, there has also been the realization that several real-world optimization problems still cannot be totally automated. Very often, user interaction is necessary for refining the optimization problem, managing the computational resources available, or validating or adjusting a computer-generated solution. This paper presents an interactive framework called user hints for having humans help optimization methods to solve difficult problems. In the framework users play a dynamic and important role by providing hints. Hints are actions that help to insert domain knowledge, to escape from local minima, to reduce the space of solutions to be explored, or to avoid ambiguity when there is more than one optimal solution. User hints are given in an intuitive way through a graphical interface. Visualization tools are also included in order to inform the user about the state of the optimization process. We discuss applications of the user hints framework to the graph drawing and the map labeling problems. An evaluation of some user hints systems indicates that optimization processes can benefit from human interaction.

A fuzzy set-based approach to origin–destination matrix estimation in urban traffic networks with imprecise data

An important issue in the management of urban traffic networks is the estimation of origin–destination (O–D) matrices whose entries represent the travel demands of network users. We discuss the challenges of O–D matrix estimation with incomplete, imprecise data. We propose a fuzzy set-based approach that utilises successive linear approximation. The fuzzy sets used have triangular membership functions that are easy to interpret and enable straightforward calibration of the parameters that weight the discrepancy between observed data and those predicted by the proposed approach. The method is potentially useful when prior O–D matrix entry estimates are unavailable or scarce, requiring trip generation information on origin departures and/or destination arrivals, leading to multiple modelling alternatives. The method may also be useful when there is no O–D matrix that can be user-optimally assigned to the network to reproduce observed link counts exactly. The method has been tested on some numerical examples from the literature and the results compare favourably with the results of earlier methods. It has also been successfully used to estimate O–D matrices for a practical urban traffic network in Brazil.

Turning restriction design in traffic networks with a budget constraint

The restriction (prohibition) of certain turns at intersections is a very common task employed by the managers of urban traffic networks. Surprisingly, this approach has received little attention in the research literature. The turning restriction design problem (TRDP) involves finding a set of turning restrictions at intersections to promote flow in a congested urban traffic network. This article uses a successive linear approximation (SLA) method for identifying approximate solutions to a nonlinear model of the TRDP. It aims to adjust the current turning restriction regime in a given network in order to minimize total user travel cost when route choice is driven by user equilibrium principles. Novel features of the method include the facts that it is based on link capacity-based arc travel costs and there is a budget constraint on the total cost of all turning restriction alterations. It has been tested using standard network examples from the literature. One of the tests utilized a multi-start approach which improved the solutions produced by the SLA method. The method was also employed to identify turning restrictions for an actual medium-sized urban traffic network in Brazil. Computational experience with the proposed method is promising.

An Evolutionary Algorithm for an Optimization Model of Edge Bundling

This paper discusses three edge bundling optimization problems that aim to minimize the total number of bundles of a graph drawing, in conjunction with other aspects, as the main goal. A novel evolutionary algorithm for edge bundling for these problems is described. The algorithm was successfully tested by solving the related problems applied to real-world instances in reasonable computational time. The development and analysis of optimization models have received little attention in the area of edge bundling. However, the reported experimental results demonstrate the effectiveness and the applicability of the proposed evolutionary algorithm to help resolve edge bundling problems by formally defining them as optimization models.

A variant of k -nearest neighbors search with cyclically permuted query points for rotation-invariant image processing

The well-known k -nearest neighbors problem ( k NN ) involves building a data structure that reports the k closest training points to each of a given set of query points, with all points being in a given metric space S . The problem discussed here is an important operation in rotation-invariant image processing. It consists of a nontrivial variant of k NN : given a set of training points X and a set of query points Y find, for each query point y ? Y , the k nearest training points to y , where the notion of distance is given by a pseudometric of S defined over cyclic permutations of y and the elements of X . The multiplicity of the query point permutations makes serial brute force search too costly for instances of practical size. We present a transformation that enables any instance of the variant to be solved as a k NN problem. Although this enables the application of any k NN algorithm, the transformation is too time costly to be practical for instances of practical dimensions. For this reason, we present a condensation algorithm for the efficient elimination of unfavorable training points (that cannot be among the k closest neighbors of y ) and an effective parallel programming approach based on the discrete Fourier transform. The significant speedup gained over brute force search on practical datasets is reported. We also provide the mathematical basis of a conjecture that, if true, would enable the speedup to be significantly improved. The application of the approach to classification by support vector machines and k -means clustering is also discussed.

An Evolutionary Algorithm for an Optimization Model of Edge Bundling.

This paper presents two edge bundling optimization problems that address minimizing the total number of bundles, in conjunction with other aspects, as the main goal. A novel evolutionary edge bundling algorithm for these problems is described. The algorithm was successfully tested by solving two related problems applied to real-world instances in reasonable computational time. The development and analysis of optimization models have received little attention in the area of edge bundling. However, the reported experimental results demonstrate the effectiveness and the applicability of the proposed evolutionary algorithm to help resolve edge bundling problems formally defined as optimization models.