Cosmic strings are topological defects which can be formed in grand unified theory scale phase
transitions in the early universe. They are also predicted to form in the context of string theory. The main
mechanism for a network of Nambu-Goto cosmic strings to lose energy is through the production of loops
and the subsequent emission of gravitational waves, thus offering an experimental signature for the
existence of cosmic strings. Here we report on the analysis conducted to specifically search for
gravitational-wave bursts from cosmic string loops in the data of Advanced LIGO 2015-2016 observing
run (O1). No evidence of such signals was found in the data, and as a result we set upper limits on the
cosmic string parameters for three recent loop distribution models. In this paper, we initially derive
constraints on the string tension Gμ and the intercommutation probability, using not only the burst analysis
performed on the O1 data set but also results from the previously published LIGO stochastic O1 analysis,
pulsar timing arrays, cosmic microwave background and big-bang nucleosynthesis experiments. We show
that these data sets are complementary in that they probe gravitational waves produced by cosmic string
loops during very different epochs. Finally, we show that the data sets exclude large parts of the parameter
space of the three loop distribution models we consider.