Graph minors. V. Excluding a planar graph
Journal of Combinatorial Theory Series B
Quickly excluding a planar graph
Journal of Combinatorial Theory Series B
Algorithms for facility location problems with outliers
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Using homogeneous weights for approximating the partial cover problem
Journal of Algorithms
Computing small partial coverings
Information Processing Letters
Graph minors. XVI. excluding a non-planar graph
Journal of Combinatorial Theory Series B
Polynomial-time data reduction for dominating set
Journal of the ACM (JACM)
Approximation algorithms for partial covering problems
Journal of Algorithms
Fixed-parameter algorithms for (k, r)-center in planar graphs and map graphs
ACM Transactions on Algorithms (TALG)
Algorithmic Graph Minor Theory: Decomposition, Approximation, and Coloring
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 refined search tree technique for Dominating Set on planar graphs
Journal of Computer and System Sciences
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
A 2 + ɛ approximation algorithm for the k-MST problem
Mathematical Programming: Series A and B
Parameterized Complexity of Vertex Cover Variants
Theory of Computing Systems
Treewidth Lower Bounds with Brambles
Algorithmica
Partial vs. Complete Domination: t-Dominating Set
SOFSEM '07 Proceedings of the 33rd conference on Current Trends in Theory and Practice of Computer Science
Parameterized Complexity for Domination Problems on Degenerate Graphs
Graph-Theoretic Concepts in Computer Science
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Improved upper bounds for vertex cover
Theoretical Computer Science
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Intuitive algorithms and t-vertex cover
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Survey: Subexponential parameterized algorithms
Computer Science Review
The Bidimensionality Theory and Its Algorithmic Applications 1
The Computer Journal
Subexponential algorithms for partial cover problems
Information Processing Letters
Structure theorem and isomorphism test for graphs with excluded topological subgraphs
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
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Covering problems are fundamental classical problems in optimization, computer science and complexity theory. Typically an input to these problems is a family of sets over a finite universe and the goal is to cover the elements of the universe with as few sets of the family as possible. The variations of covering problems include well-known problems like Set Cover, Vertex Cover, Dominating Set and Facility Location to name a few. Recently there has been a lot of study on partial covering problems, a natural generalization of covering problems. Here, the goal is not to cover all the elements but to cover the specified number of elements with the minimum number of sets. In this paper we study partial covering problems in graphs in the realm of parameterized complexity. Classical (non-partial) version of all these problems has been intensively studied in planar graphs and in graphs excluding a fixed graph H as a minor. However, the techniques developed for parameterized version of non-partial covering problems cannot be applied directly to their partial counterparts. The approach we use, to show that various partial covering problems are fixed parameter tractable on planar graphs, graphs of bounded local treewidth and graph excluding some graph as a minor, is quite different from previously known techniques. The main idea behind our approach is the concept of implicit branching. We find implicit branching technique to be interesting on its own and believe that it can be used for some other problems.