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If π k j is the probability of the region of the support in which the kth factor is the constraining factor on utility, we can write Σ x π x j min ( f 1 x j, f 2 x j,.. f Kx j ) = Σ κ π κ j Σ k ε κ π k | κ f k j where π k|κ is the probability of particular values of the kth factor given that this factor is the minimal constraining one.
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However, in many practical instances (for instance when hyperarcs only have one head node), the algorithm Minimize returns a minimal constrained hyperpath.
In general, hard instances H of the enumeration problem have to violate the condition of well-separation for same choice of R f ⊂ H, in order that the corresponding minimal constrained hyperpath problem becomes hard.
Given the hypergraph described above (whose size is linear in the size of the underlying 3-SAT problem) consider the minimal constrained hyperpath problem where all the hyperarcs ε i are mandatory, and the target is T. A solution of this problem gives in linear time a solution for the underlying SAT problem, which makes the problem of minimal constrained hyperpath an NP-complete problem.
We develop a new class of gain-constrained and power-constrained algorithms termed constrained minimal disturbance (CMD).
This software allows incorporation of multiple calibration points, fixing or constraining minimal or maximal ages to the nodes.
The recent study of Magallon and Castillo [ 111] presents a diversification hypothesis for all angiosperms derived from constraining minimal ages of 49 nodes with fossil data.
As minimizing or constraining the average shortest path of a graph is difficult, we chose to look for a minimal set that also had a small radius.
The multiperiod degree constrained minimal spanning tree (MDCMST) problem consists of scheduling the installation of links in a network so as to connect a set of terminal nodes to a central node with minimal present value of expenditures.
Build dependencies for packages should also be minimal which will constrain interface tests with other tools to static textual representations an external tool's update with a change to its default file format will not have an immediate effect.
BLP: Binary linear programming; cMCS: Constrained minimal cut set; EM: Elementary modes; EMA: Elementary mode analysis; MCS: Minimal cut set.
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