Design is as Easy as Optimization

We consider the class of max-min and min-max optimization problems subject to a global budget (or weight) constraint and we undertake a systematic algorithmic and complexitytheoretic study of such problems, which we call problems design problems. Every optimization problem leads to a natural design problem. Our main result uses techniques of Freund-Schapire [FS99] from learning theory, and its generalizations, to show that for a large class of optimization problems, the design version is as easy as the optimization version. We also observe a close relationship between design problems and packing problems; this yields relationships between fractional packing of spanning and Steiner trees in a graph, the strength of the graph, and the integrality gap of the bidirected cut relaxation for the graph.

• Type: Journal
• Year: 2010
• Where: SIAMDM
• Authors: Deeparnab Chakrabarty, Aranyak Mehta, Vijay V. Vazirani
• Keywords: Design Problems, Optimization Problems, Problems, SIAMDM 2010