Simplicial decompositions of graphs: a survey of applications
Discrete Mathematics
NC algorithms for computing the number of perfect matchings in K3,3-free graph and related problems
Information and Computation
Extending planar graph algorithms to K3,3-free graphs
Information and Computation
Sequential and parallel algorithms to find a K5 minor
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Improved Parameterized Algorithms for Planar Dominating Set
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
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
Improved Tree Decomposition Based Algorithms for Domination-like Problems
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
-Approximation for Treewidth of Graphs Excluding a Graph with One Crossing as a Minor
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
WG '01 Proceedings of the 27th International Workshop on Graph-Theoretic Concepts in Computer Science
Graph Theory With Applications
Graph Theory With Applications
Parameterized Complexity
Dominating sets in planar graphs: branch-width and exponential speed-up
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Subexponential parameterized algorithms on graphs of bounded-genus and H-minor-free graphs
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Equivalence of local treewidth and linear local treewidth and its algorithmic applications
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Polynomial-time data reduction for dominating set
Journal of the ACM (JACM)
Parameterized complexity: exponential speed-up for planar graph problems
Journal of Algorithms
Approximation algorithms for classes of graphs excluding single-crossing graphs as minors
Journal of Computer and System Sciences
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Fixed-parameter algorithms for (k, r)-center in planar graphs and map graphs
ACM Transactions on Algorithms (TALG)
A refined search tree technique for Dominating Set on planar graphs
Journal of Computer and System Sciences
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
Fast algorithms for hard graph problems: bidimensionality, minors, and local treewidth
GD'04 Proceedings of the 12th international conference on Graph Drawing
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We present a fixed-parameter algorithm that constructively solves the k-dominating set problem on graphs excluding one of K5 or K3, 3 as a minor in time O(416.5驴k nO(1)), which is an exponential factor faster than the previous O(2O(k) nO(1)). In fact, we present our algorithm for any H-minor-free graph where H is a single-crossing graph (can be drawn in the plane with at most one crossing) and obtain the algorithm for K3, 3 (K5)-minor-free graphs as a special case. As a consequence, we extend our results to several other problems such as vertex cover, edge dominating set, independent set, clique-transversal set, kernels in digraphs, feedback vertex set and a series of vertex removal problems. Our work generalizes and extends the recent result of exponential speedup in designing fixed-parameter algorithms on planar graphs by Alber et al. to other (nonplanar) classes of graphs.