Conditional lower bounds for graph sensitivity problems

Abstract

In this thesis, we show conditional lower bounds for graph distance problems in the sensitivity setting, a restriction on the dynamic setting. We consider graph diameter, radius, and eccentricities over a few distance metrics, and sensitivities both constant and logarithmic in the size of the graph. Despite these restrictions, we find that many lower bound results from the static and fully dynamic settings still hold under popular conjectures. We show many of these lower bounds for graphs with constant maximum degree as well.