Exact algorithms for L (2,1)-labeling of graphs

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Abstract

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 > 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(1.3161n). © Springer-Verlag Berlin Heidelberg 2007.

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Kratochvíl, J., Kratsch, D., & Liedloff, M. (2007). Exact algorithms for L (2,1)-labeling of graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4708 LNCS, pp. 513–524). Springer Verlag. https://doi.org/10.1007/978-3-540-74456-6_46

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