Daniel Mölle

Parameterized power domination complexity

The optimization problem of measuring all nodes in an electrical network by placing as few measurement units (PMUs) as possible is known as Power Dominating Set. Nodes can be measured indirectly according to Kirchhoffs law. We show that this problem can be solved in linear time for graphs of bounded treewidth and establish bounds on its parameterized complexity if the number of PMUs is the parameter.

Randomized Divide-and-Conquer: Improved Path, Matching, and Packing Algorithms

We propose a randomized divide-and-conquer technique that leads to improved randomized and deterministic algorithms for NP-hard path, matching, and packing problems. For the parameterized max-path problem, our randomized algorithm runs in time

Enumerate and Expand: Improved Algorithms for Connected Vertex Cover and Tree Cover

O(4^{k}k^{2.7}m)

A faster algorithm for the steiner tree problem

and polynomial space (where m is the number of edges in the input graph), improving the previous best randomized algorithm for the problem that runs in time

Algorithms based on the treewidth of sparse graphs

O(5.44^{k}km)

Partial vs. Complete Domination: t-Dominating Set

and exponential space. Our randomized algorithms for the parameterized max r-d matching and max r-set packing problems run in time

A Bound on the Pathwidth of Sparse Graphs with Applications to Exact Algorithms

4^{(r-1)k}n^{O(1)}

Enumerate and expand: new runtime bounds for vertex cover variants

and polynomial space, improving the previous best algorithms for the problems that run in time

Enumerate and expand: improved algorithms for connected vertex cover and tree cover

10.88^{rk}n^{O(1)}

Intuitive algorithms and t -vertex cover

and exponential space. Moreover, our randomized algorithms can be derandomized to result in significantly improved deterministic algorithms for the problems, and they can be extended to solve other matching and packing problems.