Work

The complexity of growing a graph

Year: 2024

Type: article

Abstract: We study a new algorithmic process of graph growth which starts from a single initial vertex and operates in discrete time-steps, called 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 are removed. Removed edges are called excess edges . The main problem investigated in this paper is: Given a target graph G , design an algorithm that outputs a process that grows G , called a growth schedule . Additionally, we aim to minimize the total number of slots k and of excess edges ℓ used by the process. We provide both positive and negative results, with our main focus being either schedules with sub-linear number of slots or with no excess edges.

Source: Journal of Computer and System Sciences

DOI: 10.1016/j.jcss.2024.103587

Authors: George Mertzios, Othon Michail, George Skretas, Paul G. Spirakis, Michail Theofilatos

Institutions: Durham University, University of Liverpool, Hasso Plattner Institute, University of Potsdam

Language: English

Topic: Complexity and Algorithms in Graphs

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,520

Funder: Engineering and Physical Sciences Research Council