Temporal Matching on Geometric Graph Data

Abstract

Temporal graphs are the modeling of pairwise and historical interaction in recordings of a dataset. A temporal matching formalizes the planning of pair working sessions of a required duration. We depict algorithms finding temporal matchings maximizing the total workload, by an exact algorithm and an approximation. The exact algorithm is a dynamic programming solving the general case in \(O^*((\gamma +1)^n)\) time, where n is the number of vertices, \(\gamma \) represents the desired duration of each pair working session, and \(O^*\) only focuses on exponential factors. When the input data is embedded in an Euclidean space, called geometric data, our approximation is based on a new notion of temporal velocity. We revise a known notion of static density [van Leeuwen, 2009] and result in a polynomial time approximation scheme for temporal geometric graphs of bounded density. We confront our implementations to known opensource implementation (Our source code is available at https://github.com/Talessseed/Temporal-matching-of-historical-and-geometric-graphs).