We address the valve location problem, one of the basic problems in design of long oil pipelines. Whenever a pipeline is depressurized, the shutoff valves block the oil flow and seal the damaged part of the pipeline. Thus, the quantity of oil possibly contaminating the area around the pipeline...

We address the valve location problem, one of the basic problems in design of long oil pipelines. Whenever a pipeline is depressurized, the shutoff valves block the oil flow and seal the damaged part of the pipeline. Thus, the quantity of oil possibly contaminating the area around the pipeline...

This paper is concerned with polynomial time approximations schemes for the generalized geometric problems with geographic clustering. We illustrate the approach on the generalized traveling salesman problem which is also known as Group-TSP or TSP with neighborhoods. We prove that under the...

We consider a revenue maximization problem where we are selling a set of m items, each of which available in a certain quantity (possibly unlimited) to a set of n bidders. Bidders are single minded, that is, each bidder requests exactly one subset, or bundle of items. Each bidder has a valuation...