Network Optimization Problems" by Alon et al. (SODA 2004)
The paper introduces a framework for maintaining fractional solutions for
online cut/connectiity problems, with competitive
ratio logarithmic in the number of edges in the graph. As a next step, one
typically performs a rounding of the fractional
solutions to integral ones, again in an online manner. I will illustrate
how the authors apply the framework to some
well known optimization problems.