Dominating sets in planar graphs: branch-width and exponential speed-up
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Practical Algorithms on Partial k-Trees with an Application to Domination-like Problems
WADS '93 Proceedings of the Third Workshop on Algorithms and Data Structures
Dynamic Programming on Graphs with Bounded Treewidth
ICALP '88 Proceedings of the 15th International Colloquium on Automata, Languages and Programming
COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
Server Placements, Roman Domination and other Dominating Set Variants
TCS '02 Proceedings of the IFIP 17th World Computer Congress - TC1 Stream / 2nd IFIP International Conference on Theoretical Computer Science: Foundations of Information Technology in the Era of Networking and Mobile Computing
Defending the Roman Empire: a new strategy
Discrete Mathematics - Special issue: The 18th British combinatorial conference
The turing way to parameterized complexity
Journal of Computer and System Sciences - Special issue on Parameterized computation and complexity
A refined search tree technique for Dominating Set on planar graphs
Journal of Computer and System Sciences
Nonblocker: parameterized algorithmics for minimum dominating set
SOFSEM'06 Proceedings of the 32nd conference on Current Trends in Theory and Practice of Computer Science
Roman domination over some graph classes
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
Parameterized Complexity
Roman Domination on 2-Connected Graphs
SIAM Journal on Discrete Mathematics
Signed Roman domination in graphs
Journal of Combinatorial Optimization
Roman domination on strongly chordal graphs
Journal of Combinatorial Optimization
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We analyse the graph-theoretic formalization of ROMAN DOMINATION, dating back to the military strategy of the Emperor Constantine, from a parameterized perspective. More specifically, we prove that this problem is W[2]-complete for general graphs. However, parameterized algorithms are presented for graphs of bounded treewidth and for planar graphs. Moreover, it is shown that a parametric dual of ROMAN DOMINATION is in FPT.