Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
Towards a syntactic characterization of PTAS
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
On fixed-parameter tractability and approximability of NP optimization problems
Journal of Computer and System Sciences - special issue on complexity theory
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Information Processing Letters
A partial k-arboretum of graphs with bounded treewidth
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On calculating connected dominating set for efficient routing in ad hoc wireless networks
DIALM '99 Proceedings of the 3rd international workshop on Discrete algorithms and methods for mobile computing and communications
Subgraph isomorphism in planar graphs and related problems
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
A polynomial-time approximation scheme for weighted planar graph TSP
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
A 2-Approximation Algorithm for the Undirected Feedback Vertex Set Problem
SIAM Journal on Discrete Mathematics
Deciding first-order properties of locally tree-decomposable structures
Journal of the ACM (JACM)
Light spanners and approximate TSP in weighted graphs with forbidden minors
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
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Dominating sets in planar graphs: branch-width and exponential speed-up
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Improved Parameterized Algorithms for Planar Dominating Set
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
Efficient Approximation for Triangulation of Minimum Treewidth
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
WG '01 Proceedings of the 27th International Workshop on Graph-Theoretic Concepts in Computer Science
WG '02 Revised Papers from the 28th International Workshop on Graph-Theoretic Concepts in Computer Science
An approximation scheme for planar graph TSP
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Building Steiner trees with incomplete global knowledge
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
New Distributed Algorithm for Connected Dominating Set in Wireless Ad Hoc Networks
HICSS '02 Proceedings of the 35th Annual Hawaii International Conference on System Sciences (HICSS'02)-Volume 9 - Volume 9
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
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
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
Bidimensional Parameters and Local Treewidth
SIAM Journal on Discrete Mathematics
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)
Graph Theory With Applications
Graph Theory With Applications
Fast algorithms for hard graph problems: bidimensionality, minors, and local treewidth
GD'04 Proceedings of the 12th international conference on Graph Drawing
Parameterized Complexity
Improved approximation algorithms for minimum-weight vertex separators
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Algorithmic Graph Minor Theory: Decomposition, Approximation, and Coloring
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
A linear-time approximation scheme for planar weighted TSP
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Subexponential parameterized algorithms on bounded-genus graphs and H-minor-free graphs
Journal of the ACM (JACM)
A subset spanner for Planar graphs,: with application to subset TSP
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Quickly deciding minor-closed parameters in general graphs
European Journal of Combinatorics
Catalan structures and dynamic programming in H-minor-free graphs
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
The Complexity Ecology of Parameters: An Illustration Using Bounded Max Leaf Number
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
Approximation Algorithms and Hardness for Domination with Propagation
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
An O(n log n) approximation scheme for Steiner tree in planar graphs
ACM Transactions on Algorithms (TALG)
Linear Kernel for Planar Connected Dominating Set
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
Approximation Algorithms via Structural Results for Apex-Minor-Free Graphs
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Journal of Discrete Algorithms
Complexity and approximation results for the connected vertex cover problem
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
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Faster approximation schemes and parameterized algorithms on H-minor-free and odd-minor-free graphs
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Fast minor testing in planar graphs
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Computational study for planar connected dominating set problem
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part II
A linear kernel for a planar connected dominating set
Theoretical Computer Science
Subexponential algorithms for partial cover problems
Information Processing Letters
Improved approximations for hard optimization problems via problem instance classification
Rainbow of computer science
Dealing with large hidden constants: engineering a planar steiner tree PTAS
Journal of Experimental Algorithmics (JEA)
Fast sub-exponential algorithms and compactness in planar graphs
ESA'11 Proceedings of the 19th European conference on Algorithms
Linear kernels for (connected) dominating set on H-minor-free graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Bidimensionality and geometric graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Fast subexponential algorithm for non-local problems on graphs of bounded genus
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Faster approximation schemes and parameterized algorithms on (odd-)H-minor-free graphs
Theoretical Computer Science
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Slightly superexponential parameterized problems
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Fast algorithms for hard graph problems: bidimensionality, minors, and local treewidth
GD'04 Proceedings of the 12th international conference on Graph Drawing
Approximation algorithms for unit disk graphs
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
Improved algorithms and complexity results for power domination in graphs
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
Algorithms for graphs embeddable with few crossings per edge
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
Towards a taxonomy of techniques for designing parameterized algorithms
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Algorithmic graph minor theory: improved grid minor bounds and wagner's contraction
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Catalan structures and dynamic programming in H-minor-free graphs
Journal of Computer and System Sciences
Survey: Subexponential parameterized algorithms
Computer Science Review
Tree decompositions of graphs: Saving memory in dynamic programming
Discrete Optimization
Graph minors and parameterized algorithm design
The Multivariate Algorithmic Revolution and Beyond
What's next? future directions in parameterized complexity
The Multivariate Algorithmic Revolution and Beyond
Subexponential parameterized algorithms
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
On the complexity of metric dimension
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
When is weighted satisfiability FPT?
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
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We demonstrate a new connection between fixed-parameter tractability and approximation algorithms for combinatorial optimization problems on planar graphs and their generalizations. Specifically, we extend the theory of so-called "bidimensional" problems to show that essentially all such problems have both subexponential fixed-parameter algorithms and PTASs. Bidimensional problems include e.g. feedback vertex set, vertex cover, minimum maximal matching, face cover, a series of vertex-removal problems, dominating set, edge dominating set, r-dominating set, diameter, connected dominating set, connected edge dominating set, and connected r-dominating set. We obtain PTASs for all of these problems in planar graphs and certain generalizations; of particular interest are our results for the two well-known problems of connected dominating set and general feedback vertex set for planar graphs and their generalizations, for which PTASs were not known to exist. Our techniques generalize and in some sense unify the two main previous approaches for designing PTASs in planar graphs, namely, the Lipton-Tarjan separator approach [FOCS'77] and the Baker layerwise decomposition approach [FOCS'83]. In particular, we replace the notion of separators with a more powerful tool from the bidimensionality theory, enabling the first approach to apply to a much broader class of minimization problems than previously possible; and through the use of a structural backbone and thickening of layers we demonstrate how the second approach can be applied to problems with a "nonlocal" structure.