In this case, we need (i) to verify that the domination number is in fact γ, and (ii) to identify the non-dominating sets of cardinality γ. Proposition 2.2 For every M≥1 and every γ≥2, let G, |V(G)|=n=Mγ, be the γ-fold lexicographic product of KM. Then γ(G)=γ ...
where | · | is the cardinality of the bacteria (B) and phages (P), and outd and ind refer to the outdegree and indegree of the nodes, that is, the number of arrows leaving source nodes (phages) or entering target nodes (bacteria), respectively. These equations consider that phages ...
An optimal CVCP3 with cardinality one is a vertex, and an optimal CVCP3 of cardinality two is an edge. After dealing with these two special cases in the first two lines of the algorithm, the remaining part is devoted to the case when an optimal CVCP3 has at least three vertices. ...
(P1) For every directed graph D = ( V, A), the minimum cardinality of a cut induced by C is equal to the maximum number of pairwise disjoint coverings for C. 2. (P2) For every directed graph D = ( V, A), and for ... A Schrijver - 《Journal of Combinatorial Theory》 被引量...
holds. A DSM with the minimum cardinality is called a minimum dominating set for multilayer networks (MDSM). Since an MDSM is also a DS for each Gi, if we select an MDSM as a set of driver nodes (with assuming that each driver node can control its links independently), every Gi become...
To find good solutions we adopt a randomized rounding strategy, which is challenging to analyze because of the cardinality constraint present in our formulation. Even though this obstacle can be overcome using dependent rounding, we show that it is possible to obtain provably good solutions using ...
Hence the inf in (31) can be replaced by a minimum. } We consider now the linear complementarity problem and establish similarly an upper bound for the cardinality of its minimum-support solution. Theorem 4.3 Upper Bounding Nonzero Elements of LCP Solutions Let S2 be the nonempty solution set...
they can be viewed as global constraints that link the objective with some other constraints of the problem. The constraint structure of many discrete optimization problems can be modeled efficiently using all different constraints. As a matter of fact, the all different con- straint was one ...
[11] showed that a maximum cardinality matching in G provides an ϱ-optimal solution to Max-ECP where ϱ is the largest cardinality of a clique in G. This is the best known performance ratio for a polynomial time approximation algorithm for the problem. Since ϱ can be O(n), the ...
If and have the same cardinality (), a natural and often used strategy is to model this task as an instance of the minimum cost perfect matching problem in bipartite graphs (MIN-PM). For this, and are viewed as node sets of a bipartite graph whose edge set E contains all prima facie...