Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Fourier meets möbius: fast subset convolution
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
A 2O (k)poly(n) algorithm for the parameterized Convex Recoloring problem
Information Processing Letters
Efficient approximation of convex recolorings
Journal of Computer and System Sciences
Improved Approximation Algorithm for Convex Recoloring of Trees
Theory of Computing Systems
Convex recolorings of strings and trees: Definitions, hardness results and algorithms
Journal of Computer and System Sciences
On exact complexity of subgraph homeomorphism
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
Partial convex recolorings of trees and galled networks: Tight upper and lower bounds
ACM Transactions on Algorithms (TALG)
Connected coloring completion for general graphs: algorithms and complexity
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
Quadratic kernelization for convex recoloring of trees
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
Parameterized Complexity
Convex Recoloring Revisited: Complexity and Exact Algorithms
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
A Kernel for Convex Recoloring of Weighted Forests
SOFSEM '10 Proceedings of the 36th Conference on Current Trends in Theory and Practice of Computer Science
The complexity of minimum convex coloring
Discrete Applied Mathematics
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A vertex coloring of a tree is called convex if each color induces a connected component. The NP-hard CONVEX RECOLORING problem on vertex-colored trees asks for a minimum-weight change of colors to achieve a convex coloring. For the non-uniformly weighted model, where the cost of changing a vertex v to color c depends on both v and c, we improve the running time on trees from O(Δκ ċ κn) to O(3κ ċ κn), where Δ is the maximum vertex degree of the input tree T, κ is the number of colors, and n is the number of vertices in T. In the uniformly weighted case, where costs depend only on the vertex to be recolored, one can instead parameterize on the number of bad colors β ≤ κ, which is the number of colors that do not already induce a connected component. Here, we improve the running time from O(Δβ ċ βn) to O(3β ċ βn). For the case where the weights are integers bounded by M, using fast subset convolution, we further improve the running time with respect to the exponential part to O(2κ ċ κ4n2M log2(nM)) and O(2β ċ β4n2M log2(nM)), respectively. Finally, we use fast subset convolution to improve the exponential part of the running time of the related 1-CONNECTED COLORING COMPLETION problem.