Approximate Shortest Distance Computing: A Query-Dependent Local Landmark Scheme

Abstract

Shortest distance query between two nodes is a fundamental operation in large-scale networks. Most existing methods in the literature take a landmark embedding approach, which selects a set of graph nodes as landmarks and computes the shortest distances from each landmark to all nodes as an embedding. To handle a shortest distance query between two nodes, the precomputed distances from the landmarks to the query nodes are used to compute an approximate shortest distance based on the triangle inequality. In this paper, we analyze the factors that affect the accuracy of the distance estimation in the landmark embedding approach. In particular we find that a globally selected, query-independent landmark set plus the triangulation based distance estimation introduces a large relative error, especially for nearby query nodes. To address this issue, we propose a query-dependent local landmark scheme, which identifies a local landmark close to the specific query nodes and provides a more accurate distance estimation than the traditional global landmark approach. Specifically, a local landmark is defined as the least common ancestor of the two query nodes in the shortest path tree rooted at a global landmark. We propose efficient local landmark indexing and retrieval techniques, which are crucial to achieve low offline indexing complexity and online query complexity. Two optimization techniques on graph compression and graph online search are also proposed, with the goal to further reduce index size and improve query accuracy. Our experimental results on large-scale social networks and road networks demonstrate that the local landmark scheme reduces the shortest distance estimation error significantly when compared with global landmark embedding.