Parameterized Complexity of Diameter

Parameterized Complexity of Diameter

Diameter—the task of computing the length of a longest shortest path—is a fundamental graph problem. Assuming the Strong Exponential Time Hypothesis, there is no O(n)time algorithm even in sparse graphs [Roditty and Williams, 2013]. To circumvent this lower bound we aim for algorithms with running time f(k)(n+m) where k is a parameter and f is a function as small as possible. For our choices of...

Parameterized computational complexity of finding small-diameter subgraphs

Finding subgraphs of small diameter in undirected graphs has been seemingly unexplored from a parameterized complexity perspective. We perform the first parameterized complexity study on the corresponding NP-hard s-Club problem. We consider two parameters: the solution size and its dual.

Parameterized complexity of firefighting

The Firefighter problem is to place firefighters on the vertices of a graph to prevent a fire with known starting point from lighting up the entire graph. In each time step, a firefighter may be placed on an unburned vertex, permanently protecting it, and the fire spreads to all neighboring unprotected vertices of burning vertices. The goal is to let as few vertices burn as possible. This probl...

Complexity of Parameterized Counting

Parameterized Complexity of Finding a Spanning Tree with Minimum Reload Cost Diameter

We study the minimum diameter spanning tree problem under the reload cost model (DiameterTree for short) introduced by Wirth and Steffan (2001). In this problem, given an undirected edge-colored graph G, reload costs on a path arise at a node where the path uses consecutive edges of different colors. The objective is to find a spanning tree of G of minimum diameter with respect to the reload co...