The complexity of growing a graph

IF 1.1 3区 计算机科学 Q1 BUSINESS, FINANCE Journal of Computer and System Sciences Pub Date : 2024-09-27 DOI:10.1016/j.jcss.2024.103587
George 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 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 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.
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图形增长的复杂性
我们研究了一种新的图形增长算法过程,它从单个初始顶点开始,以离散的时间步长(称为时隙)运行。在每个时段内,图形通过两个操作(i)顶点生成和(ii)边激活进行增长。该过程在最后一个时隙完成,在该时隙中,图形的一个(可能为空)边子集被移除。被移除的边称为多余边。本文研究的主要问题是给定目标图 G,设计一种算法,输出一个使 G 增长的过程,称为增长计划。此外,我们的目标是最小化进程使用的插槽 k 和多余边 ℓ 的总数。我们提供了正反两方面的结果,重点是具有亚线性槽数或无多余边的时间表。
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来源期刊
Journal of Computer and System Sciences
Journal of Computer and System Sciences 工程技术-计算机:理论方法
CiteScore
3.70
自引率
0.00%
发文量
58
审稿时长
68 days
期刊介绍: The Journal of Computer and System Sciences publishes original research papers in computer science and related subjects in system science, with attention to the relevant mathematical theory. Applications-oriented papers may also be accepted and they are expected to contain deep analytic evaluation of the proposed solutions. Research areas include traditional subjects such as: • Theory of algorithms and computability • Formal languages • Automata theory Contemporary subjects such as: • Complexity theory • Algorithmic Complexity • Parallel & distributed computing • Computer networks • Neural networks • Computational learning theory • Database theory & practice • Computer modeling of complex systems • Security and Privacy.
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