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ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
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
A linear-time algorithm to find a separator in a graph excluding a minor
ACM Transactions on Algorithms (TALG)
Computational study on planar dominating set problem
Theoretical Computer Science
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
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Information Processing Letters
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Improved approximations for hard optimization problems via problem instance classification
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Journal of Computer and System Sciences
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MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
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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
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Known algorithms on graphs of bounded treewidth are probably optimal
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Planar k-path in subexponential time and polynomial space
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
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LATA'12 Proceedings of the 6th international conference on Language and Automata Theory and Applications
Catalan structures and dynamic programming in H-minor-free graphs
Journal of Computer and System Sciences
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The Multivariate Algorithmic Revolution and Beyond
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Primal-dual approximation algorithms for Node-Weighted Steiner Forest on planar graphs
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Information and Computation
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This paper surveys the theory of bidimensionality. This theory characterizes a broad range of graph problems (‘bidimensional’) that admit efficient approximate or fixed-parameter solutions in a broad range of graphs. These graph classes include planar graphs, map graphs, bounded-genus graphs and graphs excluding any fixed minor. In particular, bidimensionality theory builds on the Graph Minor Theory of Robertson and Seymour by extending the mathematical results and building new algorithmic tools. Here, we summarize the known combinatorial and algorithmic results of bidimensionality theory with the high-level ideas involved in their proof; we describe the previous work on which the theory is based and/or extends; and we mention several remaining open problems.