Parameterized Complexity of Diameter

02/27/2018

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by   Matthias Bentert, et al.

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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. For our choices of k we systematically explore a hierarchy of structural graph parameters.