Abstract
Spreading processes on graphs are a natural model for a wide variety of real-world phenomena, including information spread over social networks and biological diseases spreading over contact networks. Often, the networks over which these processes spread are dynamic in nature, and can be modelled with temporal graphs. Here, we study the problem of deleting edges from a given temporal graph in order to reduce the number of vertices (temporally) reachable from a given starting point. This could be used to control the spread of a disease, rumour, etc. in a temporal graph. In particular, our aim is to find a temporal subgraph in which a process starting at any single vertex can be transferred to only a limited number of other vertices using a temporally-feasible path. We introduce a natural edge-deletion problem for temporal graphs and provide positive and negative results on its computational complexity and approximability.
Highlights
Introduction and motivationA temporal graph is, loosely speaking, a graph that changes with time
A great variety of modern and traditional networks can be modeled as temporal graphs; social networks, wired or wireless networks which change dynamically, transportation networks, and several physical systems are only a few examples of networks that change over time [31, 38]
In this paper we studied the problem of removing a small number of edges from a given temporal graph to ensure that every vertex has a temporal path to at most h other vertices
Summary
A temporal graph is, loosely speaking, a graph that changes with time. A great variety of modern and traditional networks can be modeled as temporal graphs; social networks, wired or wireless networks which change dynamically, transportation networks, and several physical systems are only a few examples of networks that change over time [31, 38]. 57:2 Deleting Edges to Restrict the Size of an Epidemic in Temporal Networks its vast applicability in many areas, this notion of temporal graphs has been studied from different perspectives under various names such as time-varying [1,24,44], evolving [11,15,22], dynamic [14, 27], and graphs over time [33]; for a recent attempt to integrate existing models, concepts, and results from the distributed computing perspective see the survey papers [12,13,14] and the references therein. We begin by describing a polynomial-time algorithm to compute an h-approximation to Min TR Edge Deletion on arbitrary temporal graphs, show how similar techniques can be applied to compute a c-approximation on inputs in which the underlying graph has cutwidth c. We note that all of our results can be applied, with minor modifications to the proofs, to the setting of (α, β)-temporal paths
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