The monadic second-order logic of graphs. I. recognizable sets of finite graphs
Information and Computation
Easy problems for tree-decomposable graphs
Journal of Algorithms
The spatial complexity of oblivious k-probe Hash functions
SIAM Journal on Computing
Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
Journal of the ACM (JACM)
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Deciding first-order properties of locally tree-decomposable structures
Journal of the ACM (JACM)
Vertex cover: further observations and further improvements
Journal of Algorithms
Splitters and near-optimal derandomization
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Algorithm Design
Parameterized Complexity
Parameterized Complexity of Cardinality Constrained Optimization Problems
The Computer Journal
Partial vs. Complete Domination: t-Dominating Set
SOFSEM '07 Proceedings of the 33rd conference on Current Trends in Theory and Practice of Computer Science
Improved Upper Bounds for Partial Vertex Cover
Graph-Theoretic Concepts in Computer Science
Parameterized Graph Cleaning Problems
Graph-Theoretic Concepts in Computer Science
Parameterized graph cleaning problems
Discrete Applied Mathematics
Segmenting strings homogeneously via trees
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
Annotating fragmentation patterns
WABI'09 Proceedings of the 9th international conference on Algorithms in bioinformatics
Parameterized complexity of even/odd subgraph problems
Journal of Discrete Algorithms
Intuitive algorithms and t-vertex cover
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Parameterized complexity of even/odd subgraph problems
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
The parameterized complexity of k-edge induced subgraphs
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Linear time algorithms for finding a dominating set of fixed size in degenerated graphs
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
Finding dense subgraphs of sparse graphs
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
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We develop a new randomized method, random separation, for solving fixed-cardinality optimization problems on graphs, i.e., problems concerning solutions with exactly a fixed number k of elements (e.g., k vertices V′) that optimize solution values (e.g., the number of edges covered by V′). The key idea of the method is to partition the vertex set of a graph randomly into two disjoint sets to separate a solution from the rest of the graph into connected components, and then select appropriate components to form a solution. We can use universal sets to derandomize algorithms obtained from this method. This new method is versatile and powerful as it can be used to solve a wide range of fixed-cardinality optimization problems for degree-bounded graphs, graphs of bounded degeneracy (a large family of graphs that contains degree-bounded graphs, planar graphs, graphs of bounded tree-width, and nontrivial minor-closed families of graphs), and even general graphs.