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Angelini, Patrizio; Da Lozzo, Giordano; Di Battista, Giuseppe; Frati, Fabrizio; Roselli, Vincenzo (2014)
Languages: English
Types: Preprint
Subjects: Computer Science - Computational Geometry, Computer Science - Data Structures and Algorithms

Classified by OpenAIRE into

ACM Ref: TheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITY, MathematicsofComputing_DISCRETEMATHEMATICS
In this paper we study two problems related to the drawing of level graphs, that is, T-LEVEL PLANARITY and CLUSTERED-LEVEL PLANARITY. We show that both problems are NP-complete in the general case and that they become polynomial-time solvable when restricted to proper instances.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • 1. Angelini, P., Da Lozzo, G., Neuwirth, D.: On the complexity of some problems related to SEFE. CoRR abs/1207.3934 (2013)
    • 2. Angelini, P., Di Battista, G., Frati, F., Patrignani, M., Rutter, I.: Testing the simultaneous embeddability of two graphs whose intersection is a biconnected or a connected graph. J. of Discrete Algorithms 14, 150-172 (2012)
    • 3. Angelini, P., Da Lozzo, G.: Deepening the relationship between SEFE and C-planarity. CoRR abs/1404.6175 (2014)
    • 4. Angelini, P., Da Lozzo, G., Neuwirth, D.: On some NP-complete SEFE problems. In: Pal, S.P., Sadakane, K. (eds.) WALCOM. LNCS, vol. 8344, pp. 200-212 (2014)
    • 5. Blasiu¨s, T., Kobourov, S.G., Rutter, I.: Simultaneous embedding of planar graphs. In: Tamassia, R. (ed.) Handbook of Graph Drawing and Visualization. CRC Press (2013)
    • 6. Bla¨sius, T., Rutter, I.: Disconnectivity and relative positions in simultaneous embeddings. In: Didimo, W., Patrignani, M. (eds.) GD'13. LNCS, vol. 7704, pp. 31-42 (2013)
    • 7. Bla¨sius, T., Rutter, I.: Simultaneous PQ-ordering with applications to constrained embedding problems. In: Khanna, S. (ed.) SODA. pp. 1030-1043. SIAM (2013)
    • 8. Eades, P., Feng, Q.W., Lin, X., Nagamochi, H.: Straight-line drawing algorithms for hierarchical graphs and clustered graphs. Algorithmica 44(1), 1-32 (2006)
    • 9. Forster, M., Bachmaier, C.: Clustered level planarity. In: van Emde Boas, P., Pokorny´, J., Bielikova´, M., Stuller, J. (eds.) SOFSEM. LNCS, vol. 2932, pp. 218-228 (2004)
    • 10. Ju¨nger, M., Leipert, S.: Level planar embedding in linear time. J. Graph Algorithms Appl. 6(1), 67-113 (2002)
    • 11. Opatrny, J.: Total ordering problem. SIAM J. Comput. 8(1), 111-114 (1979)
    • 12. Schaefer, M.: Toward a theory of planarity: Hanani-Tutte and planarity variants. J. of Graph Alg. and Appl 17(4), 367-440 (2013)
    • 13. Wotzlaw, A., Speckenmeyer, E., Porschen, S.: Generalized k-ary tanglegrams on level graphs: A satisfiability-based approach and its evaluation. Discrete Applied Mathematics 160(16-17), 2349-2363 (2012)
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