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| HAL: hal-00460873, version 1 |
| DOI: 10.1007/s00453-009-9302-7 |
| Detailed view |  Export this paper |
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| Algorithmica 59, 2 (2011) 169-194 |
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| Exact Algorithms for L(2,1)-Labeling of Graphs |
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| Frédéric Havet 1Martin Klazar 2 |
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| (2011) |
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| 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 $\{0, \dots ,k\}$ 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 $k=4$, where the running time of our algorithm is $O(1.3006^n)$. Furthermore we show that dynamic programming can be used to establish an $O(3.8730^n)$ algorithm to compute an optimal $L(2,1)$-labeling. |
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| 1: | MASCOTTE (INRIA Sophia Antipolis / Laboratoire I3S) |
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INRIA – Université de Nice Sophia Antipolis (UNS) – CNRS : UMR7271 |
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| 2: | Department of Applied Mathematics (KAM) (KAM) |
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Univerzita Karlova v Praze |
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| 3: | Laboratoire d'Informatique Théorique et Appliquée (LITA) |
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Université Paul Verlaine - Metz |
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| 4: | Laboratoire d'Informatique Fondamentale d'Orléans (LIFO) |
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Université d'Orléans : EA4022 – Ecole Nationale Supérieure d'Ingénieurs de Bourges |
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| Subject | : | Computer Science/Data Structures and Algorithms |
| hal-00460873, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00460873 | |
| oai:hal.archives-ouvertes.fr:hal-00460873 | |
| From: Mathieu Liedloff | |
| Submitted on: Tuesday, 2 March 2010 16:44:32 | |
| Updated on: Thursday, 7 July 2011 23:31:36 | |
