Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Graph minors: X. obstructions to tree-decomposition
Journal of Combinatorial Theory Series B
Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Random sampling of large planar maps and convex polyhedra
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
LEDA: a platform for combinatorial and geometric computing
LEDA: a platform for combinatorial and geometric computing
All pairs shortest paths using bridging sets and rectangular matrix multiplication
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Domination in Graphs Applied to Electric Power Networks
SIAM Journal on Discrete Mathematics
Improved Parameterized Algorithms for Planar Dominating Set
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
Polynomial-time data reduction for dominating set
Journal of the ACM (JACM)
Experimental evaluation of a tree decomposition-based algorithm for vertex cover on planar graphs
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
Subexponential parameterized algorithms on bounded-genus graphs and H-minor-free graphs
Journal of the ACM (JACM)
Dominating Sets in Planar Graphs: Branch-Width and Exponential Speed-Up
SIAM Journal on Computing
Dynamic programming and fast matrix multiplication
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Catalan structures and dynamic programming in H-minor-free graphs
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Optimal branch-decomposition of planar graphs in O(n3) Time
ACM Transactions on Algorithms (TALG)
New upper bounds on the decomposability of planar graphs
Journal of Graph Theory
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
How to use planarity efficiently: new tree-decomposition based algorithms
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
Computing branch decomposition of large planar graphs
WEA'08 Proceedings of the 7th international conference on Experimental algorithms
Efficient exact algorithms on planar graphs: exploiting sphere cut branch decompositions
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Survey: Subexponential parameterized algorithms
Computer Science Review
The Bidimensionality Theory and Its Algorithmic Applications 1
The Computer Journal
Computational study for planar connected dominating set problem
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part II
Computational study on bidimensionality theory based algorithm for longest path problem
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Hi-index | 5.23 |
Recently, there has been significant theoretical progress towards fixed-parameter algorithms for the DOMINATING SET problem of planar graphs. It is known that the problem on a planar graph with n vertices and dominating number k can be solved in O(2^O^(^k^)n) time using tree/branch-decomposition based algorithms. In this paper, we report computational results of Fomin and Thilikos algorithm which uses the branch-decomposition based approach. The computational results show that the algorithm can solve the DOMINATING SET problem of large planar graphs in a practical time and memory space for the class of graphs with small branchwidth. For the class of graphs with large branchwidth, the size of instances that can be solved by the algorithm in practice is limited to about one thousand edges due to a memory space bottleneck. The practical performances of the algorithm coincide with the theoretical analysis of the algorithm. The results of this paper suggest that the branch-decomposition based algorithms can be practical for some applications on planar graphs.