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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Comparing two geometric graphs embedded in space is important in the field of transportation network analysis. Given street maps of the same city collected from different sources, researchers often need to know how and where they differ. However, the majority of current graph comparison algorithms are based on structural properties of graphs, such as their degree distribution or their local connectivity properties, and do not consider their spatial embedding. This ignores a key property of road networks since the similarity of travel over two road networks is intimately tied to the specific spatial embedding. Likewise, many current algorithms specific to street map comparison either do not provide quality guarantees or focus on spatial embeddings only. Motivated by road network comparison, we propose a new path-based distance measure between two planar geometric graphs that is based on comparing sets of travel paths generated over the graphs. Surprisingly, we are able to show that using paths of bounded link-length, we can capture global structural and spatial differences between the graphs. We show how to utilize our distance measure as a local signature in order to identify and visualize portions of high similarity in the maps. Finally, we present an experimental evaluation of our distance measure and its local signature on street map data from Berlin, Germany and Athens, Greece. 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. Abstract Error-tolerant graph matching is a powerful concept that has various applications in pattern recognition and machine vision. In the present paper, a new distance measure on graphs is proposed. It is based on the maximal common subgraph of two graphs. The new measure is superior to edit distance based measures in that no particular edit operations together with their costs need to be defined. It is formally shown that the new distance measure is a metric. Potential algorithms for the efficient computation of the new measure are discussed. The subgraph isomorphism problem involves deciding whether a copy of a pattern graph occurs inside a larger target graph. The non-induced version allows extra edges in the target, whilst the induced version does not. Although both variants are NP-complete, algorithms inspired by constraint programming can operate comfortably on many real-world problem instances with thousands of vertices. However, they cannot handle arbitrary instances of this size. We show how to generate " really hard " random instances for subgraph isomorphism problems, which are computationally challenging with a couple of hundred vertices in the target, and only twenty pattern vertices. For the non-induced version of the problem, these instances lie on a satisfiable unsatisfiable phase transition, whose location we can predict; for the induced variant, much richer behaviour is observed, and constrained-ness gives a better measure of difficulty than does proximity to a phase transition. These results have practical consequences: we explain why the widely researched " filter verify " indexing technique used in graph databases is founded upon a misunderstanding of the empirical hardness of NP-complete problems, and cannot be beneficial when paired with any reasonable subgraph isomorphism algorithm.