The Connected Vertex Cover problem, where the goal is to compute a minimum
set of vertices in a given graph which forms a vertex cover and induces a
connected subgraph, is a fundamental combinatorial problem and has received
extensive attention in various subdomains of algorithmics. In the area of
kernelization, it is known that this problem is unlikely to have efficient
preprocessing algorithms, also known as polynomial kernelizations. However, it
has been shown in a recent work of Lokshtanov et al. [STOC 2017] that if one
considered an appropriate notion of approximate kernelization, then this
problem parameterized by the solution size does admit an approximate polynomial
kernelization. In fact, Lokhtanov et al. were able to obtain a polynomial size
approximate kernelization scheme (PSAKS) for Connected Vertex Cover
parameterized by the solution size. A PSAKS is essentially a preprocessing
algorithm whose error can be made arbitrarily close to 0. In this paper we
revisit this problem, and consider parameters that are strictly smaller than
the size of the solution and obtain the first polynomial size approximate
kernelization schemes for the Connected Vertex Cover problem when parameterized
by the deletion distance of the input graph to the class of cographs, the class
of bounded treewidth graphs, and the class of all chordal graphs.Comment: 1 figure; Revisions from the previous version incorporated based on
the comments from some anonymous reviewer
