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Algebraic tools for the construction of colored flows with boundary constraints

Marius Dorkenoo, Marie-Christine Eglin-Leclerc, Eric Rémila (2004)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We give a linear time algorithm which, given a simply connected figure of the plane divided into cells, whose boundary is crossed by some colored inputs and outputs, produces non-intersecting directed flow lines which match inputs and outputs according to the colors, in such a way that each edge of any cell is crossed by at most one line. The main tool is the notion of height function, previously introduced for tilings. It appears as an extension of the notion of potential of a flow in a planar...

Algebraic tools for the construction of colored flows with boundary constraints

Marius Dorkenoo, Marie-Christine Eglin-Leclerc, Eric Rémila (2010)

RAIRO - Theoretical Informatics and Applications

We give a linear time algorithm which, given a simply connected figure of the plane divided into cells, whose boundary is crossed by some colored inputs and outputs, produces non-intersecting directed flow lines which match inputs and outputs according to the colors, in such a way that each edge of any cell is crossed by at most one line. The main tool is the notion of height function, previously introduced for tilings. It appears as an extension of the notion of potential of a flow in...

Algorithm for the complement of orthogonal operations

Iryna V. Fryz (2018)

Commentationes Mathematicae Universitatis Carolinae

G. B. Belyavskaya and G. L. Mullen showed the existence of a complement for a k -tuple of orthogonal n -ary operations, where k < n , to an n -tuple of orthogonal n -ary operations. But they proposed no method for complementing. In this article, we give an algorithm for complementing a k -tuple of orthogonal n -ary operations to an n -tuple of orthogonal n -ary operations and an algorithm for complementing a k -tuple of orthogonal k -ary operations to an n -tuple of orthogonal n -ary operations. Also we find some...

Algorithmic aspects of total-subdomination in graphs

Laura M. Harris, Johannes H. Hattingh, Michael A. Henning (2006)

Discussiones Mathematicae Graph Theory

Let G = (V,E) be a graph and let k ∈ Z⁺. A total k-subdominating function is a function f: V → {-1,1} such that for at least k vertices v of G, the sum of the function values of f in the open neighborhood of v is positive. The total k-subdomination number of G is the minimum value of f(V) over all total k-subdominating functions f of G where f(V) denotes the sum of the function values assigned to the vertices under f. In this paper, we present a cubic time algorithm to compute the total k-subdomination...

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