Vertex partitioning problems: characterization, complexity and algorithms on partial K-trees
Vertex partitioning problems: characterization, complexity and algorithms on partial K-trees
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Algorithms for Vertex Partitioning Problems on Partial k-Trees
SIAM Journal on Discrete Mathematics
Partitioning graphs into generalized dominating sets
Nordic Journal of Computing
Algorithms for vertex-partitioning problems on graphs with fixed clique-width
Theoretical Computer Science
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized complexity of the smallest degree-constrained subgraph problem
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
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
Finding good decompositions for dynamic programming on dense graphs
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
Locally constrained graph homomorphisms-structure, complexity, and applications
Computer Science Review
Parameterized Complexity
Width Parameters Beyond Tree-width and their Applications
The Computer Journal
Graph classes with structured neighborhoods and algorithmic applications
Theoretical Computer Science
Graph classes with structured neighborhoods and algorithmic applications
Theoretical Computer Science
| Hi-index | 5.23 |
Given a graph G we provide dynamic programming algorithms for many locally checkable vertex subset and vertex partitioning problems. Their runtime is polynomial in the number of equivalence classes of problem-specific equivalence relations on subsets of vertices, defined on a given decomposition tree of G. Using these algorithms all these problems become solvable in polynomial time for many well-known graph classes like interval graphs and permutation graphs (Belmonte and Vatshelle (2013) [1]). Given a decomposition of boolean-width k we show that the algorithms will have runtime O(n^42^O^(^k^^^2^)), providing the first large class of problems solvable in fixed-parameter single-exponential time in boolean-width.