Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
On the all-pairs-shortest-path problem in unweighted undirected graphs
Journal of Computer and System Sciences - Special issue on selected papers presented at the 24th annual ACM symposium on the theory of computing (STOC '92)
On the exponent of the all pairs shortest path problem
Journal of Computer and System Sciences - Special issue: papers from the 32nd and 34th annual symposia on foundations of computer science, Oct. 2–4, 1991 and Nov. 3–5, 1993
Rectangular matrix multiplication revisited
Journal of Complexity
All pairs shortest paths using bridging sets and rectangular matrix multiplication
Journal of the ACM (JACM)
Introduction to Algorithms
Algorithms for Vertex Partitioning Problems on Partial k-Trees
SIAM Journal on Discrete Mathematics
Dominating sets in planar graphs: branch-width and exponential speed-up
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Improved Tree Decomposition Based Algorithms for Domination-like Problems
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
All Pairs Shortest Paths in Undirected Graphs with Integer Weights
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Tour Merging via Branch-Decomposition
INFORMS Journal on Computing
Computing Minimal Triangulations in Time O(n\alpha \log n) = o(n2.376)
SIAM Journal on Discrete Mathematics
Finding a maximum weight triangle in n3-Δ time, with applications
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Speeding-up linear programming using fast matrix multiplication
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Optimal branch-decomposition of planar graphs in O(n3) time
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Efficient exact algorithms on planar graphs: exploiting sphere cut branch decompositions
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Two birds with one stone: the best of branchwidth and treewidth with one algorithm
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Computational Study on Dominating Set Problem of Planar Graphs
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
Planar Feedback Vertex Set and Face Cover: Combinatorial Bounds and Subexponential Algorithms
Graph-Theoretic Concepts in Computer Science
On the minimum corridor connection problem and other generalized geometric problems
Computational Geometry: Theory and Applications
Computational study on planar dominating set problem
Theoretical Computer Science
Exponential time algorithms for the minimum dominating set problem on some graph classes
ACM Transactions on Algorithms (TALG)
Dynamic programming and planarity: Improved tree-decomposition based algorithms
Discrete Applied Mathematics
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
A linear kernel for planar feedback vertex set
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
Faster algorithms on branch and clique decompositions
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
On the Boolean-width of a graph: structure and applications
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
Computational study for planar connected dominating set problem
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part II
Fast sub-exponential algorithms and compactness in planar graphs
ESA'11 Proceedings of the 19th European conference on Algorithms
Connectivity is not a limit for kernelization: planar connected dominating set
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
A strengthened analysis of an algorithm for Dominating Set in planar graphs
Discrete Applied Mathematics
Survey: Subexponential parameterized algorithms
Computer Science Review
Graph minors and parameterized algorithm design
The Multivariate Algorithmic Revolution and Beyond
Subexponential parameterized algorithms
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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We give a novel general approach for solving NP-hard optimization problems that combines dynamic programming and fast matrix multiplication. The technique is based on reducing much of the computation involved to matrix multiplication. We show that our approach works faster than the usual dynamic programming solution for any vertex subset problem on graphs of bounded branchwidth. In particular, we obtain the fastest algorithms for Planar Independent Set of runtime O(22.52√n), for PLANAR DOMINATING SET of runtime exact O(23.99√n) and parameterized O(211.98√k)ċ nO(1), and for PLANAR HAMILTONIAN Cycle of runtime O(25.58√n). The exponent of the running time is depending heavily on the running time of the fastest matrix multiplication algorithm that is currently o(n2.376).