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Polynomial-Size Binary Decision Diagrams for the Exactly Half-d-Hyperclique Problem Reading Each Input Bit Twice

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Abstract

A binary decision diagram (BDD) is a graph-based data structure representing Boolean functions; ℓ-BDDs are BDDs with an additional restriction that each input bit can be tested at most ℓ times. A d-uniform hypergraph H on N vertices is an exactly half-d-hyperclique if N/2 of its vertices form a hyperclique and the remaining vertices are isolated. Wegener [J. ACM 35(2), 461–471 (1988)] conjectured that there is no polynomial-size (d−1)-BDD for the Exactly half-d-hyperclique problem. We refute this conjecture by constructing polynomial-size (syntactic) 2-BDDs for the Exactly half-d-hyperclique problem for every d≥2.

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  1. Department of Applied Mathematics and Institute for Theoretical Computer Science (ITI), Faculty of Mathematics and Physics, Charles University, Malostranské náměstí 25, 118 00, Prague 1, Czech Republic

    Daniel Král’

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  1. Daniel Král’
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Correspondence to Daniel Král’.

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Institute for Theoretical Computer Science (ITI) is supported by Ministry of Education of Czech Republic as projects LN00A056 and 1M0545.

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Král’, D. Polynomial-Size Binary Decision Diagrams for the Exactly Half-d-Hyperclique Problem Reading Each Input Bit Twice. Theory Comput Syst 45, 27–42 (2009). https://doi.org/10.1007/s00224-007-9067-9

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