Fast exact algorithm for L(2, 1)-labeling of graphs

Authors:
Konstanty Junosza-Szaniawski;Jan Kratochvíl;Mathieu Liedloff;Peter Rossmanith;Paweł Rzazewski
Affiliations:
Warsaw University of Technology, Faculty of Mathematics and Information Science, Warszawa, Poland;Department of Applied Mathematics, and Institute for Theoretical Computer Science, Charles University,Praha, Czech Republic;Laboratoire d'Informatique Fondamentale d'Orléans, Université d'Orléans, Orléans Cedex, France;Department of Computer Science, RWTH Aachen University, Germany;Warsaw University of Technology, Faculty of Mathematics and Information Science, Warszawa, Poland
Venue:
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
Year:
2011

Citing 14
Cited 2

Labelling graphs with a condition at distance 2

SIAM Journal on Discrete Mathematics
The $L(2,1)$-Labeling Problem on Graphs

SIAM Journal on Discrete Mathematics
Fixed parameter complexity of λ-labelings

Discrete Applied Mathematics - special issue on the 25th international workshop on graph theoretic concepts in computer science (WG'99)
The L(h, k)-Labelling Problem: A Survey and Annotated Bibliography

The Computer Journal
The Channel Assignment Problem with Variable Weights

SIAM Journal on Discrete Mathematics
L(2,1)-labelling of graphs

Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Graph labellings with variable weights, a survey

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

Algorithmica
Exact Exponential Algorithms

Exact Exponential Algorithms
On improved exact algorithms for L(2, 1)-labeling of graphs

IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
Measure and conquer: domination – a case study

ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Distance constrained labelings of graphs of bounded treewidth

ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Locally constrained graph homomorphisms-structure, complexity, and applications

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

MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science

Determining the l(2,1)-span in polynomial space

WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
Fast exact algorithm for L(2,1)-labeling of graphs

Theoretical Computer Science

Quantified Score

Hi-index	0.00

Visualization

Abstract

An L(2, 1)-labeling of a graph is a mapping from its vertex set into nonnegative integers such that the labels assigned to adjacent vertices differ by at least 2, and labels assigned to vertices of distance 2 are different. The span of such a labeling is the maximum label used, and the L(2, 1)-span of a graph is the minimum possible span of its L(2, 1)- labelings. We show how to compute the L(2, 1)-span of a connected graph in time O*(2.6488n). Previously published exact exponential time algorithms were gradually improving the base of the exponential function from 4 to the so far best known 3.2361, with 3 seemingly having been the Holy Grail.