Scheduling algorithms for multihop radio networks
IEEE/ACM Transactions on Networking (TON)
Code assignment for hidden terminal interference avoidance in multihop packet radio networks
IEEE/ACM Transactions on Networking (TON)
A very simple algorithm for estimating the number of k-colorings of a low-degree graph
Random Structures & Algorithms
Coloring powers of planar graphs
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
On the Complexity of Distance-2 Coloring
ICCI '92 Proceedings of the Fourth International Conference on Computing and Information: Computing and Information
IWDC '02 Proceedings of the 4th International Workshop on Distributed Computing, Mobile and Wireless Computing
On Radiocoloring Hierarchically Specified Planar Graphs: PSPACE-Completeness and Approximations
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
Complexity of Partial Covers of Graphs
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
WG '02 Revised Papers from the 28th International Workshop on Graph-Theoretic Concepts in Computer Science
k-L(2,1)-labelling for planar graphs is NP-complete for k≥4
Discrete Applied Mathematics
Generalized powers of graphs and their algorithmic use
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
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The Frequency Assignment Problem (FAP) in radio networks is the problem of assigning frequencies to transmitters exploiting frequency reuse while keeping signal interference to acceptable levels. The FAP is usually modelled by variations of the graph coloring problem. The Radiocoloring (RC) of a graph G(V, E) is an assignment function Φ : V → IN such that |Φ(u) - Φ(v)| ≥ 2, when u, v are neighbors in G, and |Φ(u) - Φ(v)| ≥ 1 when the minimum distance of u, v in G is two. The discrete number and the range of frequencies used are called order and span, respectively. The optimization versions of the Radiocoloring Problem (RCP) are to minimize the span or the order. In this paper we prove that the min span RCP is NP-complete for planar graphs. Next, we provide an O(nΔ) time algorithm (|V| = n) which obtains a radiocoloring of a planar graph G that approximates the minimum order within a ratio which tends to 2 (where Δ the maximum degree of G). Finally, we provide a fully polynomial randomized approximation scheme (fpras) for the number of valid radiocolorings of a planar graph G with λ colors, in the case λ ≥ 4Δ + 50.