New Algorithms for Mixed Dominating Set

A mixed dominating set is a collection of vertices and edges that dominates all graph. We study the complexity exact parameterized algorithms for \textsc{Mixed Dominating Set}, resolving some open questions. In particular, we settle problem's by treewidth pathwidth giving an algorithm running in time $O^*(5^{tw})$ (improving current best $O^*(6^{tw})$), as well lower bound showing our cannot be improved under Strong Exponential Time Hypothesis (SETH), even if $O^*((2 - \varepsilon)^{pw})$). Furthermore, using simple but so far overlooked observation on structure minimal solutions, obtain branching which improve both known FPT this problem, from $O^*(4.172^k)$ to $O^*(3.510^k)$, exponential-time algorithm, $O^*(2^n)$ exponential space, $O^*(1.912^n)$ polynomial space.