The Computer Journal
Domination numbers of planar graphs
Journal of Graph Theory
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
The complexity of shortest path and dilation bounded interval routing
Theoretical Computer Science
The Compactness of Interval Routing
SIAM Journal on Discrete Mathematics
Theoretical Computer Science
Approximate Distance Labeling Schemes
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
New bounds for multi-label interval routing
Theoretical Computer Science
Fixed-parameter algorithms for (k, r)-center in planar graphs and map graphs
ACM Transactions on Algorithms (TALG)
Problems from CGCS Luminy, May 2007
European Journal of Combinatorics
Fixed-parameter algorithms for the (k, r)-center in planar graphs and map graphs
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
An improved interval routing scheme for almost all networks based on dominating cliques
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Augmenting outerplanar graphs to meet diameter requirements
CATS '12 Proceedings of the Eighteenth Computing: The Australasian Theory Symposium - Volume 128
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A subset of nodes S in a graph G is called k-dominating if, for every node u of the graph, the distance from u to S is at most k. We consider the parameter 驴k(G) defined as the cardinality of the smallest k-dominating set of G. For planar graphs, we show that for every 驴 0 and for every k (5/7 + 驴)D, 驴k(G) = O(1/驴). For several subclasses of planar graphs of diameter D, we show that 驴k(G) is bounded by a constant for k D/2. We conjecture that the same result holds for every planar graph. This problem is motivated by the design of routing schemes with compact data structures.