Parameterized Complexity of Diameter

Matthias Bentert (TU Berlin)

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^1.99)-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. We investigate which parameters allow for such running times. To this end, we systematically explore a hierarchy of structural graph parameters.

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