Subexponential parameterized algorithms for degree-constrained subgraph problems on planar graphs

Authors:
Ignasi Sau;Dimitrios M. Thilikos
Affiliations:
Mascotte joint Project of INRIA/CNRS/UNSA, Sophia-Antipolis, France and Graph Theory and Combinatorics Group, Departament de Matemítica Aplicada IV, UPC, Barcelona, Spain;Department of Mathematics, National and Kapodistrian University of Athens, Greece
Venue:
Journal of Discrete Algorithms
Year:
2010

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Abstract

We present subexponential parameterized algorithms on planar graphs for a family of problems of the following shape: given a graph, find a connected (induced) subgraph with bounded maximum degree and with maximum number of edges (or vertices). These problems are natural generalisations of the Longest Path problem. Our approach uses bidimensionality theory combined with novel dynamic programming techniques over branch decompositions of the input graph. These techniques can be applied to a more general family of problems that deal with finding connected subgraphs under certain degree constraints.