Minimum Spanning Tree on Spatio-Temporal Networks

TL;DR

This paper introduces novel algorithms for identifying time-intervals of minimum spanning trees in spatio-temporal networks with piecewise linear edge weights, addressing challenges of non-stationary edge rankings.

Contribution

It proposes new algorithms that handle both separable and non-separable edge weight functions in large spatio-temporal networks for TSMST computation.

Findings

Algorithms effectively identify TSMST in large networks.

Handles both separable and non-separable edge weights.

Addresses non-stationary edge ranking challenges.

Abstract

Given a spatio-temporal network (ST network) where edge properties vary with time, a time-sub-interval minimum spanning tree (TSMST) is a collection of minimum spanning trees of the ST network, where each tree is associated with a time interval. During this time interval, the total cost of tree is least among all the spanning trees. The TSMST 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, we propose 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.