Journal of the ACM (JACM)
Linear Time Solvable Optimization Problems on Graphs of Bounded Clique Width
WG '98 Proceedings of the 24th International Workshop on Graph-Theoretic Concepts in Computer Science
Storing a sparse table with O(1) worst case access time
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Parameterized Complexity
Partial vs. Complete Domination: t-Dominating Set
SOFSEM '07 Proceedings of the 33rd conference on Current Trends in Theory and Practice of Computer Science
Efficient algorithms for clique problems
Information Processing Letters
Finding paths of length k in O∗(2k) time
Information Processing Letters
A Problem Kernelization for Graph Packing
SOFSEM '09 Proceedings of the 35th Conference on Current Trends in Theory and Practice of Computer Science
The parameterized complexity of the induced matching problem
Discrete Applied Mathematics
Limits and Applications of Group Algebras for Parameterized Problems
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Algorithm for Finding k-Vertex Out-trees and Its Application to k-Internal Out-branching Problem
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
On problems without polynomial kernels
Journal of Computer and System Sciences
Randomized disposal of unknowns and implicitly enforced bounds on parameters
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
An O*(3.523k) parameterized algorithm for 3-set packing
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
Finding monotone paths in edge-ordered graphs
Discrete Applied Mathematics
An O*(3.533k)-time parameterized algorithm for the 3-set packing problem
Theoretical Computer Science
Exact parameterized multilinear monomial counting via k-layer subset convolution and k-disjoint
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Iterative Expansion and Color Coding: An Improved Algorithm for 3D-Matching
ACM Transactions on Algorithms (TALG)
Sharp separation and applications to exact and parameterized algorithms
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Faster algorithms for finding and counting subgraphs
Journal of Computer and System Sciences
Greedy localization and color-coding: improved matching and packing algorithms
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Kernel bounds for path and cycle problems
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
Improved algorithms for weighted and unweighted set splitting problems
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
Parameterized complexity of induced h-matching on claw-free graphs
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Finding the minimum-weight k-path
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
Kernel bounds for path and cycle problems
Theoretical Computer Science
| Hi-index | 0.00 |
We introduce divide-and-color, a new technique for the solution of hard graph problems. It is a combination of the well-known divide-and-conquer paradigm and color-coding [2]. Our approach first randomly colors all edges or nodes of a graph black and white, and then solves the problem recursively on the two induced parts. We demonstrate this technique by giving new randomized algorithms for the solution of two important problems. These yield runtime bounds of O*(4k) for finding a simple path of length k and O*(4( h−−1) k) for finding k edge-disjoint (resp. vertex-disjoint) copies of a graph H with h edges (resp. h nodes) in a given graph. Derandomization gives deterministic algorithms for these problems with running times O*(24 k) and O*(24hk), respectively. All these results significantly improve over the currently known best bounds. In particular, our generic algorithms beat specialized ones that have been designed to find k triangles or paths of length two.