Parameterised Bounds on the Sum of Variables in Time-Series Constraints

Abstract

For two families of time-series constraints with the aggregator Sum and features one and width, we provide parameterised sharp lower and upper bounds on the sum of the time-series variables wrt these families of constraints. This is important in many applications, as this sum represents the cost, for example the energy used, or the manpower effort expended. We use these bounds not only to gain a priori knowledge of the overall cost of a problem, we can also use them on increasing prefixes and suffixes of the variables to avoid infeasible partial assignments under a given cost budget. Experiments show that the bounds drastically reduce the effort to find cost limited solutions. This publication has emanated from research conducted with the financial support of Science Foundation Ireland under Grant number 12/RC/2289-P2 which is co-funded under the European Regional Development Fund as well as from the Gaspard-Monge program.