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Partial order with duality and consistent choice problem. (English) Zbl 0890.06002
The problem of consistent choice in a finite disjoint system of non-empty sets is considered. Any pair of chosen elements has to fulfill a given binary relation of consistency. The width of the system is the maximal cardinality of its members. The consistent choice problem is NP-complete for width \(>2\).
A connection between the consistent choice of width \(2\) and partially ordered sets with a unary operation of duality is described. Two \(O(n^2)\) algorithms for solving the consistent choice of width \(2\) are proposed on the base of the above connection. A condition is given under which the algorithms work also for width \(>2\).
MSC:
06A06 Partial orders, general
68Q25 Analysis of algorithms and problem complexity
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