Scheduling algorithms for multihop radio networks
IEEE/ACM Transactions on Networking (TON)
Drawing graphs in the plane with high resolution
SIAM Journal on Computing
Algorithms for Square Roots of Graphs
SIAM Journal on Discrete Mathematics
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
A new approach to the minimum cut problem
Journal of the ACM (JACM)
Zero knowledge and the chromatic number
Journal of Computer and System Sciences - Eleventh annual conference on structure and complexity 1996
On the Complexity of Distance-2 Coloring
ICCI '92 Proceedings of the Fourth International Conference on Computing and Information: Computing and Information
Improved Upper Bounds for λ-Backbone Colorings Along Matchings and Stars
SOFSEM '07 Proceedings of the 33rd conference on Current Trends in Theory and Practice of Computer Science
k-L(2,1)-labelling for planar graphs is NP-complete for k≥4
Discrete Applied Mathematics
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The Frequency Assignment Problem (FAP) in radio networks is the problem of assigning frequencies to transmitters, by exploiting frequency reuse while keeping signal interference to acceptable levels. The FAP is usually modelled by variations of the graph coloring problem. A Radiocoloring (RC) of a graph G(V, E) is an assignment function Φ : V → N such that |Φ(u) - Φ(v) | ≥ 2, when u, v are neighbors in G, and |Φ(u) - Φ(v)| ≥ 1 when the distance of u, v in G is two. The number of discrete frequencies 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 radiocoloring problem for general graphs is hard to approximate (unless NP = ZPP) within a factor of n1/2-ε (for any ε 0), where n is the number of vertices of the graph. However, when restricted to some special cases of graphs, the problem becomes easier. 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 where λ ≥ 4Δ + 50.