Decomposability Sample Clauses

Decomposability. The Aggregate algorithm can be decomposed into 2 algorithms Aggregate1 and Aggregate2, such that the following hold: { } { } → • Aggregate1(pp, vk1, . . . , vkn , m, σ1, . . . , σq ) Ssig, where Ssig is of size poly(log n, n) and Aggregate1 is deterministic. • Aggregate2(pp, m, Ssig) → σ, i.e., aggregate the signatures in Ssig into a new signature σ. A

Decomposability i,l From a practical point of view, the difficulty of MDPC mainly stems from the interrelationship among various subsets of decision variables. Indeed, the selection of carrier contracts in each period t ∈ T (expressed by the values of the variables αt ) restricts the candidate facilities that can be used in period t (variables vt ) and hence, the quantities that can be shipped in the same period (variables q t i,k ). Moreover, the contracts signed with carriers usually extend over several periods which creates a linkage between the decisions made in successive periods. These observations suggest that appropriate solution methodologies may be developed by relaxing some of the interrelationships mentioned above in various ways. In particular, when feasible values are set for the decision variables αt , finding the optimal values of (vt , qt ) becomes a time-separable

Decomposability i,l From a practical point of view, the difficulty of MDPC mainly stems from the interrelationship among various subsets of decision variables. Indeed, the selection of carrier contracts in each period t ∈ T (expressed by the values of the variables αt ) restricts the candidate facilities that can be used in period t (variables vt ) and hence, the quantities that can be shipped in the same period (variables q t i,k ). Moreover, the contracts signed with carriers usually extend over several periods which creates a linkage between the decisions made in successive periods. These observations suggest that appropriate solution methodologies may be developed by relaxing some of the interrelationships mentioned above in various ways. In particular, when feasible values are set for the decision variables αt , finding the optimal values of (vt , qt ) becomes a time-separable e i,l i,k sub-problem which is easier to handle, even though it remains theoretically hard. This suggests that Xxxxxxx decomposition can be useful for tackling the complex structure of the problem. An exact method based on this idea is presented in Section 6. Similarly, when we relax the constraints (6)-(9), which bind consecutive periods for each contract, the distribution sub-problem can be independently tackled for each period. Section 7 describes a heuristic algorithm based on this idea.