Map construction methods automatically produce and or update street map datasets using vehicle tracking data. Enabled by the ubiquitous generation of geo-referenced tracking data, there has been a recent surge in map construction algorithms coming from different computer science domains. A cross-comparison of the various algorithms is still very rare, since (i) algorithms and constructed maps are generally not publicly available and (ii) there is no standard approach to assess the result quality, given the lack of benchmark data and quantitative evaluation methods. This work represents a first comprehensive attempt to benchmark such map construction algorithms. We provide an evaluation and comparison of seven algorithms using four datasets and four different evaluation measures. In addition to this comprehensive comparison, we make our datasets, source code of map construction algorithms and evaluation measures publicly available on http: mapconstruction.org. . This site has been established as a repository for map construction data and algorithms and we invite other researchers to contribute by uploading code and benchmark data supporting their contributions to map construction algorithms.
In the graph theory literature, there are various distance measures for comparing two abstract graphs, that do not necessarily have a geometric embedding @cite_11 @cite_48 @cite_37 . Most closely related to street map comparison are the subgraph isomorphism problem and the maximum common isomorphic subgraph problem, both of which are NP-complete. These, however, rely on one-to-one mappings of graphs or subgraphs, and they do not take any geometric embedding into account. Graph edit distance @cite_28 @cite_15 is a way to allow noise by seeking a sequence of edit operations to transform one graph into the other, however it is NP-hard as well. @cite_52 consider a graph edit distance for geometric graphs (embedded in two different coordinate systems, however), and also show that it is NP-hard to compute.
@cite_37 @cite_28 @cite_48 @cite_52 @cite_15 @cite_11
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The graph isomorphism problem—to devise a good algorithm for determining if two graphs are isomorphic—is of considerable practical importance, and is also of theoretical interest due to its relationship to the concept of NP-completeness. No efficient (i.e., polynomial-bound) algorithm for graph isomorphism is known, and it has been conjectured that no such algorithm can exist. Many papers on the subject have appeared, but progress has been slight; in fact, the intractable nature of the problem and the way that many graph theorists have been led to devote much time to it, recall those aspects of the four-color conjecture which prompted Harary to rechristen it the “four-color disease.” This paper surveys the present state of the art of isomorphism testing, discusses its relationship to NP-completeness, and indicates some of the difficulties inherent in this particularly elusive and challenging problem. A comprehensive bibliography of papers relating to the graph isomorphism problem is given. Inexact graph matching has been one of the significant research foci in the area of pattern analysis. As an important way to measure the similarity between pairwise graphs error-tolerantly, graph edit distance (GED) is the base of inexact graph matching. The research advance of GED is surveyed in order to provide a review of the existing literatures and offer some insights into the studies of GED. Since graphs may be attributed or non-attributed and the definition of costs for edit operations is various, the existing GED algorithms are categorized according to these two factors and described in detail. After these algorithms are analyzed and their limitations are identified, several promising directions for further research are proposed. This annotated bibliography contains 32 papers on graph isomorphism not included in the bibliography of Read and Corneil, most of which discuss algorithms or their theoretical foundations. We include articles by Miller, Weisfeiler, and Whitney as well as algorithms by Johnson and Leighton, Schmidt and Druffel, Tinhofer, and Erdos and Babai. What does it mean for two geometric graphs to be similar? We propose a distance for geometric graphs that we show to be a metric, and that can be computed by solving an integer linear program. We also present experiments using a heuristic distance function. Graph data have become ubiquitous and manipulating them based on similarity is essential for many applications. Graph edit distance is one of the most widely accepted measures to determine similarities between graphs and has extensive applications in the fields of pattern recognition, computer vision etc. Unfortunately, the problem of graph edit distance computation is NP-Hard in general. Accordingly, in this paper we introduce three novel methods to compute the upper and lower bounds for the edit distance between two graphs in polynomial time. Applying these methods, two algorithms AppFull and AppSub are introduced to perform different kinds of graph search on graph databases. Comprehensive experimental studies are conducted on both real and synthetic datasets to examine various aspects of the methods for bounding graph edit distance. Result shows that these methods achieve good scalability in terms of both the number of graphs and the size of graphs. The effectiveness of these algorithms also confirms the usefulness of using our bounds in filtering and searching of graphs. A recent paper posed the question: "Graph Matching: What are we really talking about?". Far from providing a definite answer to that question, in this paper we will try to characterize the role that graphs play within the Pattern Recognition field. To this aim two taxonomies are presented and discussed. The first includes almost all the graph matching algorithms proposed from the late seventies, and describes the different classes of algorithms. The second taxonomy considers the types of common applications of graph-based techniques in the Pattern Recognition and Machine Vision field.