Multi-parameter Analysis for Local Graph Partitioning Problems: Using Greediness for Parameterization.

We study the parameterized complexity of a broad class of problems called 'local graph partitioning problems' that includes the classical fixed cardinality problems as max $$k$$ - vertex cover, $$k$$ - densest subgraph, etc. By developing a technique that we call 'greediness-for-parameterization', we obtain fixed parameter algorithms with respect to a pair of parameters $$k$$ , the size of the solution (but not its value) and $$\varDelta $$ , the maximum degree of the input graph. In particular, greediness-for-parameterization improves asymptotic running times for these problems upon random separation (that is a special case of color coding) and is more intuitive and simple. Then, we show how these results can be easily extended for getting standard-parameterization results (i.e., with parameter the value of the optimal solution) for a well known local graph partitioning problem. [ABSTRACT FROM AUTHOR]