The complexity of L(p,q)-Edge-Labelling
Gaetan Berthe, Barnaby Martin, Daniel Paulusma, Siani Smith
TL;DR
This paper establishes the computational complexity of the L(p,q)-Edge-Labelling problem, proving it is NP-complete for all non-trivial parameter values, thus completing the classification of its complexity.
Contribution
It provides a complete complexity classification of the L(p,q)-Edge-Labelling problem for all nonnegative p and q, showing NP-completeness except for the trivial case.
Findings
L(p,q)-Edge-Labelling is NP-complete for all non-trivial p,q
Existence of an integer k making L(p,q)-Edge-k-Labelling NP-complete
Completes the complexity classification of the problem
Abstract
We consider the L(p,q)-Edge-Labelling problem, which is the edge variant of the well-known L(p,q)-Labelling problem. So far, the complexity of this problem was only partially classified. We complete this study for all nonnegative p and q, by showing that, whenever (p,q) is not (0,0), L(p,q)-Edge-Labelling problem is NP-complete. We do this by proving that for all nonnegative p and q, except p=q=0, there exists an integer k so that L(p,q)-Edge-k-Labelling is NP-complete.
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Taxonomy
Topicsgraph theory and CDMA systems · Digital Image Processing Techniques · Data Mining Algorithms and Applications