Parameterized Algorithms for Colored Clustering

In the Colored Clustering problem, one is asked to cluster edge-colored (hyper-)graphs whose colors represent interaction types. More specifically, goal select as many edges possible without choosing two that share an endpoint and are colored differently. Equivalently, can also be described assigning vertices in a way fits edge-coloring well possible. As this problem NP-hard, we build on previous work by studying its parameterized complexity. We give 2ᴼ⁽ᵏ⁾·nᴼ⁽¹⁾-time algorithm where k number of selected n vertices. prove existence kernel size O(k⁵ᐟ²), resolving open posed literature. consider parameters smaller than k, selected, r, deleted. Such obtained considering difference between or r some lower bound these values. both algorithms bounds for with such parameterizations. Finally, settle complexity respect structural graph showing it W[1]-hard vertex cover tree-cut width, but fixed-parameter tractable local feedback edge number.