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Finding the shortest path in road networks becomes one of important issues in location based services (LBS). The problem of finding the optimal meeting point for a group of users has also been well studied in existing works. In this paper, we investigate a new problem for two users. Each user has his/her own source and destination. However, whether to meet before going to their destinations is with some uncertainty. We model it as minimum path pair ( MPP) query, which consists of two pairs of source and destination and a user-specified weight $\alpha$ to balance the two different needs. The result is a pair of paths connecting the two sources and destinations respectively, with minimal overall cost of the two paths and the shortest route between them. To solve MPP queries, we devise algorithms by enumerating node pairs. We adopt a location-based pruning strategy to reduce the number of node pairs for enumeration. An efficient algorithm based on point-to-point shortest path calculation is proposed to further improve query efficiency. We also give two fast approximate algorithms with approximation bounds. Extensive experiments are conducted to show the effectiveness and efficiency of our methods. [ABSTRACT FROM AUTHOR]

Motivated by the needs such as group relationship analysis, this paper introduces a new operation on graphs, named top-k path join, which discovers the top-k simple shortest paths between two given node sets. Rather than discovering the top-k simple paths between each node pair, this paper proposes a holistic join method which answers the top-k path join by finding constrained top-k simple shortest paths between two nodes, and then devises an efficient method to handle the latter problem. Specifically, we transform the graph by encoding the precomputed shortest paths to the target node, and use the transformed graph in the candidate path searching. We show that the candidate path searching on the transformed graph not only has the same result as that on the original graph but also can be terminated much earlier with the aid of precomputed results. We also discuss two other optimization strategies, including considering the join constraint in the candidate path generation as early as possible, and pruning search space in each candidate path generation with an adaptively determined threshold. The final extensive experimental results also show that our method offers a significant performance improvement over existing ones. [ABSTRACT FROM AUTHOR]

The increasing popularity of social networks has initiated a fertile research area in information extraction and data mining. Anonymization of these social graphs is important to facilitate publishing these data sets for analysis by external entities. Prior work has concentrated mostly on node identity anonymization and structural anonymization. But with the growing interest in analyzing social networks as a weighted network, edge weight anonymization is also gaining importance. We present Anónimos, a Linear Programming-based technique for anonymization of edge weights that preserves linear properties of graphs. Such properties form the foundation of many important graph-theoretic algorithms such as shortest paths problem, k-nearest neighbors, minimum cost spanning tree, and maximizing information spread. As a proof of concept, we apply Anónimos to the shortest paths problem and its extensions, prove the correctness, analyze complexity, and experimentally evaluate it using real social network data sets. Our experiments demonstrate that Anónimos anonymizes the weights, improves k-anonymity of the weights, and also scrambles the relative ordering of the edges sorted by weights, thereby providing robust and effective anonymization of the sensitive edge-weights. We also demonstrate the composability of different models generated using Anónimos, a property that allows a single anonymized graph to preserve multiple linear properties. [ABSTRACT FROM AUTHOR]