Landmark routing for large graphs in fixed-memory environments

Point-to-point shortest path distance queries are a core operation in graph analytics. However, preprocessing algorithms that speed up these queries rely on large data structures for reference. In this paper, we discuss the computational challenge introduced by these data structures when using landmark-based preprocessing algorithms on large graphs. We introduce a new heuristic for the A∗ algorithm that references a data structure of size θ(L² + V), where L represents a set of strategically chosen landmark vertices and V the set of vertices in the graph. This heuristic's benefits are permitted by an approach for computing lower bounds based on generalized polygon inequalities. In this approach, each landmark stores the distances between the landmark and vertices within its graph partition. The heuristic is experimentally compared with a previous landmark heuristic in a fixed-memory environment, as an analog to an embedded system. The new heuristic demonstrates a reduction in overall computational time and memory requirements in this environment.