197 research outputs found

    An Algorithmic Framework for Labeling Road Maps

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    Given an unlabeled road map, we consider, from an algorithmic perspective, the cartographic problem to place non-overlapping road labels embedded in their roads. We first decompose the road network into logically coherent road sections, e.g., parts of roads between two junctions. Based on this decomposition, we present and implement a new and versatile framework for placing labels in road maps such that the number of labeled road sections is maximized. In an experimental evaluation with road maps of 11 major cities we show that our proposed labeling algorithm is both fast in practice and that it reaches near-optimal solution quality, where optimal solutions are obtained by mixed-integer linear programming. In comparison to the standard OpenStreetMap renderer Mapnik, our algorithm labels 31% more road sections in average.Comment: extended version of a paper to appear at GIScience 201

    EFFICIENT GREEDY-FACE-GREEDY GEOGRAPHIC ROUTING PROTOCOLS IN MOBILE AD HOC AND SENSOR NETWORKS

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    This thesis describes and develops two planarization algorithms for geographic routing and a geographic routing protocol for mobile ad hoc and sensor networks. As all nodes are mobile and there is no fixed infrastructure, the design of routing protocols is one of the most challenging issues in mobile ad hoc and sensor networks. In recent years, greedyface- greedy (GFG) geographic routing protocols have been widely used, which need nodes to construct planar graphs as the underlying graphs for face routing. Two kinds of planarization algorithms have been developed, idealized and realistic planarization algorithms, respectively. The idealized planarization algorithms make the ideal assumption that the original network graph is a unit-disk graph (UDG). On the other hand, the realistic planarization algorithms do not need the original network to be a UDG. We propose an idealized planarization algorithm, which constructs an Edge Constrained Localized Delaunay graph (ECLDel). Compared to the existing planarized localized Delaunay graph [42], the construction of an ECLDel graph is far simpler, which reduces the communication cost and saves the network bandwidth. We propose a Pre-Processed Cross Link Detection Protocol (PPCLDP), which generates a planar spanning subgraph of the original network graph in realistic environments with obstacles. The proposed PPCLDP outperforms the existing Cross Link Detection Protocol [32] with much lower communication cost and better convergence time. In GFG routing protocols, greedy routing may fail at concave nodes, in which case, face routing is applied to recover from the greedy routing failure. This may cause extra hops in routing in networks containing voids. We propose a Hill-Area-Restricted (HAR) routing protocol, which avoids the extra hops taken in the original GFG routing. Compared to the existing Node Elevation Ad hoc Routing [4], the proposed HAR guarantees the packet delivery and decreases the communication cost greatly

    Two new approximation algorithms for the maximum planar subgraph problem

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    The maximum planar subgraph problem (MPS) is defined as follows: given a graph G, find a largest planar subgraph of G. The problem is NP-hard and it has applications in graph drawing and resource location optimization. Călinescu et al. [J. Alg. 27, 269-302 (1998)] presented the first approximation algorithms for MPS with nontrivial performance ratios. Two algorithms were given, a simple algorithm which runs in linear time for bounded-degree graphs with a ratio 7/18 and a more complicated algorithm with a ratio 4/9. Both algorithms produce outerplanar subgraphs. In this article we present two new versions of the simpler algorithm. The first new algorithm still runs in the same time, produces outerplanar subgraphs, has at least the same performance ratio as the original algorithm, but in practice it finds larger planar subgraphs than the original algorithm. The second new algorithm has similar properties to the first algorithm, but it produces only planar subgraphs. We conjecture that the performance ratios of our algorithms are at least 4/9 for MPS. We experimentally compare the new algorithms against the original simple algorithm. We also apply the new algorithms for approximating the thickness and outerthickness of a graph. Experiments show that the new algorithms produce clearly better approximations than the original simple algorithm by Călinescu et al

    Drawing Activity Diagrams

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    Activity diagrams experience an increasing importance in the design and description of software systems. Unfortunately, previous approaches for automatic layout support fail or are just insufficient to capture the complexity of the related requirements. We propose a new approach tailored to the needs of activity diagrams which combines the advantages of two fundamental layout concepts called "Sugiyama's approach" and "topology-shape-metrics approach", originally developed for layered layouts of directed graphs and for orthogonal layout of undirected graphs respectively
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