Total Ordering Problem

Abstract

Previous article Total Ordering ProblemJ. OpatrnyJ. Opatrnyhttps://doi.org/10.1137/0208008PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractThe problem of finding a total ordering of a finite set satisfying a given set of in-between restrictions is considered. It is shown that the problem is $NP$-complete.[1] Alfred V. Aho, , John E. Hopcroft and , Jeffrey D. Ullman, The design and analysis of computer algorithms, Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1975x+470 MR0413592 (54:1706) 0326.68005 Google Scholar[2] S. A. Cook, The complexity of theorem-proving procedures, Third Annual ACM Symposium on Theory of Computing, Association for Computing Machinery, New York, 1971, 151–158 0253.68020 Google Scholar[3] V. Chvatal and , G. Thomassen, Distances in orientations of graphs, Research report, STAN-CS-75-511, Stanford University, Stanford, CA, 1975 Google Scholar[4] Richard M. Karp, R. E. Miller and , J. W. Thatcher, Reducibility among combinatorial problemsComplexity of computer computations (Proc. Sympos., IBM Thomas J. Watson Res. Center, Yorktown Heights, N.Y., 1972), Plenum, New York, 1972, 85–103 MR0378476 (51:14644) CrossrefGoogle Scholar[5] D. E. Knuth, The Art of Computer Programming, Vol. 1, Addison-Wesley, Reading, MA, 1968 0191.17903 Google Scholar[6] L. Lovász, Coverings and coloring of hypergraphs, Proceedings of the Fourth Southeastern Conference on Combinatorics, Graph Theory, and Computing (Florida Atlantic Univ., Boca Raton, Fla., 1973), Utilitas Math., Winnipeg, Man., 1973, 3–12 MR0363980 (51:235) Google ScholarKeywordsalgorithmscomputational complexitytotal ordering$NP$-completeness Previous article FiguresRelatedReferencesCited ByDetails A Note on the Intersection of Alternately Orientable Graphs and Cocomparability GraphsIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, Vol. E105.A, No. 9 | 1 Sep 2022 Cross Ref Current Challenges in Infinite-Domain Constraint Satisfaction: Dilemmas of the Infinite Sheep2022 IEEE 52nd International Symposium on Multiple-Valued Logic (ISMVL) | 1 May 2022 Cross Ref On the Complexity of Recognizing Wheeler GraphsAlgorithmica, Vol. 84, No. 3 | 10 January 2022 Cross Ref StreamTable: An Area Proportional Visualization for Tables with Flowing StreamsWALCOM: Algorithms and Computation | 16 March 2022 Cross Ref Recognizing k-Clique Extendible OrderingsAlgorithmica, Vol. 83, No. 11 | 26 July 2021 Cross Ref Good orientations of unions of edge‐disjoint spanning treesJournal of Graph Theory, Vol. 96, No. 4 | 19 October 2020 Cross Ref Stable roommates with narcissistic, single-peaked, and single-crossing preferencesAutonomous Agents and Multi-Agent Systems, Vol. 34, No. 2 | 11 September 2020 Cross Ref On the Complexity of Computing TreebreadthAlgorithmica, Vol. 82, No. 6 | 12 December 2019 Cross Ref Recognizing k-Clique Extendible OrderingsGraph-Theoretic Concepts in Computer Science | 9 October 2020 Cross Ref Simultaneous EmbeddingBeyond Planar Graphs | 1 October 2020 Cross Ref Multi-source data repairing powered by integrity constraints and source reliabilityInformation Sciences, Vol. 507 | 1 Jan 2020 Cross Ref Beyond level planarity: Cyclic, torus, and simultaneous level planarityTheoretical Computer Science, Vol. 804 | 1 Jan 2020 Cross Ref Condorcet domains satisfying Arrow’s single-peakednessJournal of Mathematical Economics, Vol. 84 | 1 Oct 2019 Cross Ref Extending partial representations of circle graphsJournal of Graph Theory, Vol. 91, No. 4 | 17 December 2018 Cross Ref The complexity of shelflistingTheory and Decision, Vol. 86, No. 1 | 12 October 2018 Cross Ref Coordinate systems for supergenomesAlgorithms for Molecular Biology, Vol. 13, No. 1 | 24 September 2018 Cross Ref Expansion of gene clusters, circular orders, and the shortest Hamiltonian path problemJournal of Mathematical Biology, Vol. 77, No. 2 | 19 December 2017 Cross Ref A Sample-Based Approximate Ranking Method for Large Graphs2018 Sixth International Conference on Advanced Cloud and Big Data (CBD) | 1 Aug 2018 Cross Ref Common intervals and permutation reconstruction from MinMax -betweenness constraintsJournal of Discrete Algorithms, Vol. 49 | 1 Mar 2018 Cross Ref Upward Partitioned Book EmbeddingsGraph Drawing and Network Visualization | 21 January 2018 Cross Ref Ranking Specific Sets of ObjectsDatenbank-Spektrum, Vol. 17, No. 3 | 11 September 2017 Cross Ref Asking the Metaquestions in Constraint TractabilityACM Transactions on Computation Theory, Vol. 9, No. 3 | 9 Oct 2017 Cross Ref Acyclicity in edge-colored graphsDiscrete Mathematics, Vol. 340, No. 2 | 1 Feb 2017 Cross Ref Permutation reconstruction from MinMax -Betweenness constraintsDiscrete Applied Mathematics, Vol. 207 | 1 Jul 2016 Cross Ref Bounded Embeddings of Graphs in the PlaneCombinatorial Algorithms | 9 August 2016 Cross Ref Beyond Level PlanarityGraph Drawing and Network Visualization | 8 December 2016 Cross Ref Computing NodeTrix Representations of Clustered GraphsGraph Drawing and Network Visualization | 8 December 2016 Cross Ref Satisfiability of Ordering CSPs above Average is Fixed-Parameter Tractable2015 IEEE 56th Annual Symposium on Foundations of Computer Science | 1 Oct 2015 Cross Ref Advancements on SEFE and Partitioned Book Embedding problemsTheoretical Computer Science, Vol. 575 | 1 Apr 2015 Cross Ref Topological BirkhoffTransactions of the American Mathematical Society, Vol. 367, No. 4 | 8 August 2014 Cross Ref The importance of being properTheoretical Computer Science, Vol. 571 | 1 Mar 2015 Cross Ref Sequence Covering Arrays and Linear ExtensionsCombinatorial Algorithms | 7 June 2015 Cross Ref The Importance of Being ProperProgress in Pattern Recognition, Image Analysis, Computer Vision, and Applications | 1 Jan 2014 Cross Ref An electromagnetism metaheuristic for solving the Maximum Betweenness ProblemApplied Soft Computing, Vol. 13, No. 2 | 1 Feb 2013 Cross Ref Sequence Covering ArraysYeow Meng Chee, Charles J. 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Algorithms and Techniques Cross Ref Volume 8, Issue 1| 1979SIAM Journal on Computing History Submitted:15 September 1977Published online:31 July 2006 InformationCopyright © 1979 © Society for Industrial and Applied MathematicsKeywordsalgorithmscomputational complexitytotal ordering$NP$-completenessPDF Download Article & Publication DataArticle DOI:10.1137/0208008Article page range:pp. 111-114ISSN (print):0097-5397ISSN (online):1095-7111Publisher:Society for Industrial and Applied Mathematics