As Close as It Gets

Mike Behrisch (1) , Miki Hermann (2) , Stefan Mengel (3) , Gernot Salzer (4)

1 TU Dresden - Technische Universität Dresden = Dresden University of Technology
2 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
3 CRIL - Centre de Recherche en Informatique de Lens
4 Institut für Computersprachen

We study the minimum Hamming distance between distinct satisfying assignments of a conjunctive input formula over a given set of Boolean relations (???????????????????, ???). We present a complete classification of the complexity of this optimization problem with respect to the relations admitted in the formula. We give polynomial time algorithms for several classes of constraint languages. For all other cases we prove hardness or completeness with respect to poly-APX, or NPO, or equivalence to a well-known hard optimization problem.

Domains: Artificial Intelligence [cs.AI]

Mike Behrisch, Miki Hermann, Stefan Mengel, Gernot Salzer. As Close as It Gets. 10th International Workshop on Algorithms and Computation (WALCOM '16), 2016, Kathmandu, Nepal. pp.222--235. ⟨hal-03300998⟩