# Progressive Algorithms for Domination and Independence

@inproceedings{Fabianski2019ProgressiveAF, title={Progressive Algorithms for Domination and Independence}, author={Grzegorz Fabianski and Michał Pilipczuk and Sebastian Siebertz and Szymon Toruńczyk}, booktitle={STACS}, year={2019} }

We consider a generic algorithmic paradigm that we call progressive exploration, which can be used to develop simple and efficient parameterized graph algorithms. We identify two model-theoretic properties that lead to efficient progressive algorithms, namely variants of the Helly property and stability. We demonstrate our approach by giving linear-time fixed-parameter algorithms for the distance-r dominating set problem (parameterized by the solution size) in a wide variety of restricted graph… Expand

#### 9 Citations

Algorithmic Properties of Sparse Digraphs

- Computer Science, Mathematics
- STACS
- 2019

It is shown that the directed Steiner tree problem is fixed-parameter tractable on any class of directed bounded expansion parameterized by the number of non-terminals plus the maximal diameter in the subgraph induced by the terminals, and thereby highlights a rich algorithmic structure theory ofdirected bounded expansion classes. Expand

Distributed Domination on Graph Classes of Bounded Expansion

- Computer Science, Mathematics
- SPAA
- 2018

A new constant factor approximation algorithm for the (connected) \mboxdistance- r dominating set problem on graph classes of bounded expansion, based on a distributed computation of sparse neighborhood covers of small radius on bounded expansion classes. Expand

Nowhere dense graph classes and algorithmic applications. A tutorial at Highlights of Logic, Games and Automata 2019

- Mathematics, Computer Science
- ArXiv
- 2019

These notes, prepared for a tutorial at Highlights of Logic, Games and Automata 2019, are a brief introduction to the theory of nowhere denseness, driven by algorithmic applications. Expand

Rankwidth meets stability

- Computer Science, Mathematics
- SODA
- 2021

Monadic stability and monadic dependence extend classical structural notions for graphs by viewing them in a wider, model-theoretical context by proving that classes with bounded rankwidth excluding some half-graph as a semi-induced subgraph are linearly $\chi$-bounded. Expand

Parameterized Distributed Complexity Theory: A logical approach

- Computer Science
- ArXiv
- 2019

This work defines the levels of the Distributed-W-hierarchy and the Distributes that have first-order model-checking problems as their complete problems via suitable reductions and follows a logical approach that leads to a more robust theory. Expand

Clustering powers of sparse graphs

- Computer Science, Mathematics
- Electron. J. Comb.
- 2020

It is proved that if G is a sparse graph and d in N is fixed, then thedth power of G can be partitioned into cliques so that contracting each of these clique to a single vertex again yields a sparse graphs. Expand

Constant Round Distributed Domination on Graph Classes with Bounded Expansion

- Computer Science
- SIROCCO
- 2021

We show that the dominating set problem admits a constant factor approximation in a constant number of rounds in the LOCAL model of distributed computing on graph classes with bounded expansion. This… Expand

On the Parameterized Complexity of Reconfiguration of Connected Dominating Sets

- Computer Science, Mathematics
- IPEC
- 2020

The parameterized complexity of the Connected Dominating Set Reconfiguration problem is studied, and it is shown that the CDS-R parameterized by $k$ is fixed-parameter tractable, and in fact admits a polynomial kernel on planar graphs. Expand

Linear rankwidth meets stability

- Computer Science, Mathematics
- SODA
- 2020

This work takes both views on classes with bounded linear rankwidth and proves structural and model theoretic properties of these classes, and shows a strong link between these graph classes considered from the point of view of structural graph theory and finite model theory. Expand

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