{"title":"Exploration of k-edge-deficient temporal graphs","authors":"Thomas Erlebach, Jakob T. Spooner","doi":"10.1007/s00236-022-00421-5","DOIUrl":null,"url":null,"abstract":"<div><p>A temporal graph with lifetime <i>L</i> is a sequence of <i>L</i> graphs <span>\\(G_1, \\ldots ,G_L\\)</span>, called layers, all of which have the same vertex set <i>V</i> but can have different edge sets. The underlying graph is the graph with vertex set <i>V</i> that contains all the edges that appear in at least one layer. The temporal graph is always connected if each layer is a connected graph, and it is <i>k</i>-edge-deficient if each layer contains all except at most <i>k</i> edges of the underlying graph. For a given start vertex <i>s</i>, a temporal exploration is a temporal walk that starts at <i>s</i>, traverses at most one edge in each layer, and visits all vertices of the temporal graph. We show that always-connected, <i>k</i>-edge-deficient temporal graphs with sufficient lifetime can always be explored in <span>\\(O(kn \\log n)\\)</span> time steps. We also construct always-connected, <i>k</i>-edge-deficient temporal graphs for which any exploration requires <span>\\(\\varOmega (n \\log k)\\)</span> time steps. For always-connected, 1-edge-deficient temporal graphs, we show that <i>O</i>(<i>n</i>) time steps suffice for temporal exploration.</p></div>","PeriodicalId":7189,"journal":{"name":"Acta Informatica","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2022-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00236-022-00421-5.pdf","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Informatica","FirstCategoryId":"94","ListUrlMain":"https://link.springer.com/article/10.1007/s00236-022-00421-5","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, INFORMATION SYSTEMS","Score":null,"Total":0}
引用次数: 2
Abstract
A temporal graph with lifetime L is a sequence of L graphs \(G_1, \ldots ,G_L\), called layers, all of which have the same vertex set V but can have different edge sets. The underlying graph is the graph with vertex set V that contains all the edges that appear in at least one layer. The temporal graph is always connected if each layer is a connected graph, and it is k-edge-deficient if each layer contains all except at most k edges of the underlying graph. For a given start vertex s, a temporal exploration is a temporal walk that starts at s, traverses at most one edge in each layer, and visits all vertices of the temporal graph. We show that always-connected, k-edge-deficient temporal graphs with sufficient lifetime can always be explored in \(O(kn \log n)\) time steps. We also construct always-connected, k-edge-deficient temporal graphs for which any exploration requires \(\varOmega (n \log k)\) time steps. For always-connected, 1-edge-deficient temporal graphs, we show that O(n) time steps suffice for temporal exploration.
期刊介绍:
Acta Informatica provides international dissemination of articles on formal methods for the design and analysis of programs, computing systems and information structures, as well as related fields of Theoretical Computer Science such as Automata Theory, Logic in Computer Science, and Algorithmics.
Topics of interest include:
• semantics of programming languages
• models and modeling languages for concurrent, distributed, reactive and mobile systems
• models and modeling languages for timed, hybrid and probabilistic systems
• specification, program analysis and verification
• model checking and theorem proving
• modal, temporal, first- and higher-order logics, and their variants
• constraint logic, SAT/SMT-solving techniques
• theoretical aspects of databases, semi-structured data and finite model theory
• theoretical aspects of artificial intelligence, knowledge representation, description logic
• automata theory, formal languages, term and graph rewriting
• game-based models, synthesis
• type theory, typed calculi
• algebraic, coalgebraic and categorical methods
• formal aspects of performance, dependability and reliability analysis
• foundations of information and network security
• parallel, distributed and randomized algorithms
• design and analysis of algorithms
• foundations of network and communication protocols.