
Constant round distributed domination on graph classes with bounded expansion
We show that the dominating set problem admits a constant factor approxi...
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On distance rdominating and 2rindependent sets in sparse graphs
Dvorak (2013) gave a bound on the minimum size of a distance r dominatin...
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Distributed Reconfiguration of Maximal Independent Sets
Consider the following problem: given a graph and two maximal independen...
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Greedy domination on bicliquefree graphs
The greedy algorithm for approximating dominating sets is a simple metho...
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Deterministic CONGEST Algorithm for MDS on Bounded Arboricity Graphs
We provide a deterministic CONGEST algorithm to constant factor approxim...
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Experimental evaluation of kernelization algorithms to Dominating Set
The theoretical notions of graph classes with bounded expansion and that...
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Domination above rindependence: does sparseness help?
Inspired by the potential of improving tractability via gap or abovegu...
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Distributed Distancer Dominating Set on Sparse HighGirth Graphs
The dominating set problem and its generalization, the distancer dominating set problem, are among the wellstudied problems in the sequential settings. In distributed models of computation, unlike for domination, not much is known about distancer domination. This is actually the case for other important closelyrelated covering problem, namely, the distancer independent set problem. By result of Kuhn et al. we know the distributed domination problem is hard on high girth graphs; we study the problem on a slightly restricted subclass of these graphs: graphs of bounded expansion with high girth, i.e. their girth should be at least 4r + 3. We show that in such graphs, for every constant r, a simple greedy CONGEST algorithm provides a constantfactor approximation of the minimum distancer dominating set problem, in a constant number of rounds. More precisely, our constants are dependent to r, not to the size of the graph. This is the first algorithm that shows there are nontrivial constant factor approximations in constant number of rounds for any distance rcovering problem in distributed settings. To show the dependency on r is inevitable, we provide an unconditional lower bound showing the same problem is hard already on rings. We also show that our analysis of the algorithm is relatively tight, that is any significant improvement to the approximation factor requires new algorithmic ideas.
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