An Incremental Model for Combinatorial Minimization

Traditional optimization algorithms are concerned with static input, static constraints, and attempt to produce static output of optimal value. Recent literature has strayed from this conventional approach to deal with more realistic situations in which the input changes over time. Incremental optimization is a new framework for handling this type of dynamic behavior. We consider a general model for producing incremental versions of traditional covering problems along with several natural incremental metrics. Using this model, we demonstrate how to convert conventional algorithms into incremental algorithms with only a constant factor loss in approximation power. We introduce incremental versions of min cut, edge cover, and (k, r)-center and present some hardness results. Lastly, we discuss how the incremental model can help us more fully understand online problems and their corresponding algorithms.