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Communication Dans Un Congrès Année : 2007

Exact Algorithms for L(2,1)-Labeling of Graphs

Résumé

The notion of distance constrained graph labelings, motivated by the Frequency Assignment Problem, reads as follows: A mapping from the vertex set of a graph $G=(V,E)$ into an interval of integers $[0..k]$ is an $L(2,1)$-labeling of $G$ of span $k$ if any two adjacent vertices are mapped onto integers that are at least 2 apart, and every two vertices with a common neighbor are mapped onto distinct integers. It is known that for any fixed $k\ge 4$, deciding the existence of such a labeling is an NP-complete problem. We present exact exponential time algorithms that are faster than the naive $O((k+1)^n)$ algorithm that would try all possible mappings. The improvement is best seen in the first NP-complete case of $k=4$ -- here the running time of our algorithm is $O(1.3161^n)$.

Dates et versions

hal-00460771 , version 1 (02-03-2010)

Identifiants

Citer

Jan Kratochvil, Dieter Kratsch, Mathieu Liedloff. Exact Algorithms for L(2,1)-Labeling of Graphs. MFCS'2007 : 32nd International Symposium on Mathematical Foundations of Computer Science, Aug 2007, Cesky Krumlov, Czech Republic. pp.513-524, ⟨10.1007/978-3-540-74456-6_46⟩. ⟨hal-00460771⟩

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