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arXiv · 2107.14126

The Complexity of Growing a Graph

George B. Mertzios·Othon Michail·George Skretas·Paul G. Spirakis·Michail Theofilatos
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Abstract

We study a new algorithmic process of graph growth which starts from a single initial vertex and operates in discrete time-steps, called \emph{slots}. In every slot, the graph grows via two operations (i) vertex generation and (ii) edge activation. The process completes at the last slot where a (possibly empty) subset of the edges of the graph will be removed. Removed edges are called \emph{excess edges}. The main problem investigated in this paper is: Given a target graph $G$, we are asked to design an algorithm that outputs such a process growing $G$, called a \emph{growth schedule}. Additionally, the algorithm should try to minimize the total number of slots $k$ and of excess edges $\ell$ used by the process. We provide both positive and negative results for different values of $k$ and $\ell$, with our main focus being either schedules with sub-linear number of slots or with zero excess edges.

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George B. Mertzios, Othon Michail, George Skretas, Paul G. Spirakis, Michail Theofilatos. 2021-07-29. The Complexity of Growing a Graph. https://arxiv.org/abs/2107.14126

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