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Communication Dans Un Congrès Année : 2015

On the most imbalanced orientation of a graph

Résumé

We study the problem of orienting the edges of a graph such that the minimum over all the vertices of the absolute difference between the outdegree and the indegree of a vertex is maximized. We call this minimum the imbalance of the orientation, i.e. the higher it gets, the more imbalanced the orientation is. We study this problem denoted by MaxIm. We first present different characterizations of the graphs for which the optimal objective value of MaxIm is zero. Next we show that it is generally NP-complete and cannot be approximated within a ratio of 1/2+ε for any constant ε>0 in polynomial time unless P=NP even if the minimum degree of the graph δ equals 2. Finally we describe a polynomial-time approximation algorithm whose ratio is equal to 1/2 for graphs where δ≡0[4] or δ≡1[4] and (1/2−1/δ) for general graphs.
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Dates et versions

hal-01497825 , version 1 (29-03-2017)

Identifiants

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Walid Ben-Ameur, Antoine Glorieux, José Neto. On the most imbalanced orientation of a graph. COCOON 2015 : 21st International Conference on Computing and Combinatorics, Aug 2015, Beijing, China. pp.16 - 29, ⟨10.1007/978-3-319-21398-9_2⟩. ⟨hal-01497825⟩
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