  Cosmic strings are topological defects which can be formed in GUT-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 $G\mu$ 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.
