Leveraging High Dimensional Spatial Graph Embedding as a Heuristic for Graph Algorithms

Spatial graph embedding is a technique for placing graphs in space used for visualization and graph analytics. The general goal is to place connected nodes close together while spreading apart all others. Previous work has looked at spatial graph embedding in 2 or 3 dimensions. These used high performance libraries and fast algorithms for N-body simulation. We expand into higher dimensions to find what it can be useful for. Using an arbitrary number of dimensions allows all unweighted graph to have exact edge lengths, as n nodes can all be one distance part in a n − 1 dimensional simplex. This increases the complexity of the simulation, so we provide an efficient GPU implementation in high dimensions. Although high dimensional embeddings cannot be easily visualized they find a consistent structure which can be used for graph analytics. Problems this has been used to solve are graph isomorphism and graph coloring.