Minimum Spanning Tree on Spatio-Temporal Networks

Abstract

Given a spatio-temporal network (ST network) whose edge properties vary with time, a time-sub-interval minimum spanning tree (TSMST) is a collection of distinct minimum spanning trees of the ST network. The TSMST computation problem aims to identify a collection of distinct minimum spanning trees and their respective time-sub-intervals under the constraint that the edge weight functions are piecewise linear. This is an important problem in ST network application domains such as wireless sensor networks (e.g., energy efficient routing). Computing TSMST is challenging because the ranking of candidate spanning trees is non-stationary over a given time interval. Existing methods such as dynamic graph algorithms and kinetic data structures assume separable edge weight functions. In contrast, this paper proposes novel algorithms to find TSMST for large ST networks by accounting for both separable and non-separable piecewise linear edge weight functions. The algorithms are based on the ordering of edges in edge-order-intervals and intersection points of edge weight functions.