Abstract
As a notion dual to Knuth's nested formulas [4], we call a boolean formula\(\Phi = \mathop \wedge \limits_{i = 1}^n c_i \) in conjunctive normal formco-nested if its clauses can be linearly ordered (sayC={c i ;i=1,2, ...,n})so that the graphG cl Φ =(X∪C, {xc i ;x∈c i or ¬x∈c i } ∪ {c i c i+1;i=1, 2, ...,n}) allows a noncrossing drawing in the plane so that the circlec 1,c 2, ...,c n bounds the outerface. Our main result is that maximum satisfiability of co-nested formulas can be decided in linear time.
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References
Fellows, M.R., Kratochvíl, J., Middendorf, M., Pfeiffer, F.: The computational complexity of induced minors and related problems. Algorithmica (to appear 1993)
Garey, M.R., Johnson, D.S., Tarjan, R.E.: The planar Hamiltonian circuit problem is NP-complete. SIAM J. Comput.5, 704–714 (1976)
Hopcroft, J.E., Tarjan, R.E.: Efficient planarity testing. J. Assoc. Comput. Mach.21, 549–568 (1974)
Knutz, D.E.: Nested satisfiability. Acta Inf.28, 1–6 (1990)
Kratochvíl, J., Neŝetřil, J., Lubiw, A.: Noncrossing subgraphs of topological layouts. SIAM J. Discrete Math.4, 223–244 (1991)
Lichtenstein, D.: Planar formulae and their uses. SIAM J. Comput.11, 329–343 (1982)
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Both authors acknowledge a partial support of Ec Cooperative Action IC-1000 (project ALTEC:Algorithms for Future Technologies).
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Kratochvíl, J., Křivánek, M. Satisfiability of co-nested formulas. Acta Informatica 30, 397–403 (1993). https://doi.org/10.1007/BF01209713
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DOI: https://doi.org/10.1007/BF01209713