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We study the parameterized complexity of a broad class of problems called"local graph partitioning problems" that includes the classical fixedcardinality problems as max k-vertex cover, k-densest subgraph, etc. Bydeveloping a technique "greediness-for-parameterization", we obtain fixedparameter algorithms with respect to a pair of parameters k, the size of thesolution (but not its value) and \Delta, the maximum degree of the input graph.In particular, greediness-for-parameterization improves asymptotic runningtimes for these problems upon random separation (that is a special case ofcolor coding) and is more intuitive and simple. Then, we show how these resultscan be easily extended for getting standard-parameterization results (i.e.,with parameter the value of the optimal solution) for a well known local graphpartitioning problem.

Multi-parameter complexity analysis for constrained size graph problems: using greediness for parameterization