Heuristics for Spreading Alarm throughout a Network

Abstract

This paper provides heuristic methods for obtaining a burning number, which is a graph parameter measuring the speed of the spread of alarm, information, or contagion. For discrete time steps, the heuristics determine which nodes (centers, hubs, vertices, users) should be alarmed (in other words, burned) and in which order, when afterwards each alarmed node alarms its neighbors in the network at the next time step. The goal is to minimize the number of discrete time steps (i.e., time) it takes for the alarm to reach the entire network, so that all the nodes in the networks are alarmed. The burning number is the minimum number of time steps (i.e., number of centers in a time sequence alarmed “from outside”) the process must take. Since the problem is NP complete, its solution for larger networks or graphs has to use heuristics. The heuristics proposed here were tested on a wide range of networks. The complexity of the heuristics ranges in correspondence to the quality of their solution, but all the proposed methods provided a significantly better solution than the competing heuristic.