Amalgamation of graph transformations: a synchronization mechanism
Journal of Computer and System Sciences
A simple lower bound on edge coverings by cliques
Discrete Mathematics
Handbook of graph grammars and computing by graph transformation: volume I. foundations
Handbook of graph grammars and computing by graph transformation: volume I. foundations
Handbook of graph grammars and computing by graph transformation: vol. 3: concurrency, parallelism, and distribution
Handbook of Theoretical Computer Science
Handbook of Theoretical Computer Science
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Fundamentals of Algebraic Graph Transformation (Monographs in Theoretical Computer Science. An EATCS Series)
Invitation to data reduction and problem kernelization
ACM SIGACT News
Data reduction and exact algorithms for clique cover
Journal of Experimental Algorithmics (JEA)
Graph-grammars: An algebraic approach
SWAT '73 Proceedings of the 14th Annual Symposium on Switching and Automata Theory (swat 1973)
A Bound on the Pathwidth of Sparse Graphs with Applications to Exact Algorithms
SIAM Journal on Discrete Mathematics
Kernelization: New Upper and Lower Bound Techniques
Parameterized and Exact Computation
Confluence of graph transformation revisited
Processes, Terms and Cycles
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Kernelization is a core tool of parameterized algorithmics for coping with computationally intractable problems. A kernelization reduces in polynomial time an input instance to an equivalent instance whose size is bounded by a function only depending on some problem-specific parameter k; this new instance is called problem kernel. Typically, problem kernels are achieved by performing efficient data reduction rules. So far, there was little study in the literature concerning the mutual interaction of data reduction rules, in particular whether data reduction rules for a specific problem always lead to the same reduced instance, no matter in which order the rules are applied. This corresponds to the concept of confluence from the theory of rewriting systems. We argue that it is valuable to study whether a kernelization is confluent, using the NP-hard graph problems (Edge) Clique Cover and Partial Clique Cover as running examples. We apply the concept of critical pair analysis from graph transformation theory, supported by the AGG software tool. These results support the main goal of our work, namely, to establish a fruitful link between (parameterized) algorithmics and graph transformation theory, two so far unrelated fields.