Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Invitation to data reduction and problem kernelization
ACM SIGACT News
On the complexity of constructing Golomb Rulers
Discrete Applied Mathematics
Fixed-parameter tractability results for feedback set problems in tournaments
Journal of Discrete Algorithms
Towards Fully Multivariate Algorithmics: Some New Results and Directions in Parameter Ecology
Combinatorial Algorithms
Kernelization: New Upper and Lower Bound Techniques
Parameterized and Exact Computation
A kernelization algorithm for d-Hitting Set
Journal of Computer and System Sciences
A new algorithm for Golomb ruler derivation and proof of the 19 mark ruler
IEEE Transactions on Information Theory
Parameterized Complexity
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Golomb rulers are special rulers where for any two marks it holds that the distance between them is unique. They find applications in positioning of radio channels, radio astronomy, communication networks, and bioinformatics. An important subproblem in constructing "compact" Golomb rulers is Golomb Subruler (GSR), which asks whether it is possible to make a given ruler Golomb by removing at most k marks. We initiate a study of GSR from a parameterized complexity perspective. In particular, we develop a hypergraph characterization of rulers and consider the construction and structure of the corresponding hypergraphs. We exploit their properties to derive polynomial-time data reduction rules that lead to a problem kernel for GSR with O(k3) marks. Finally, we provide a simplified NP-hardness construction for GSR.