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 k we systematically explore a hierarchy of structural graph parameters.