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One trivial instance will do: I recall how film stars were tacitly impeded from buying property in haute bourgeois areas like Bombay's Malabar Hill until the late 1970s, and were forced, instead, to live in plush mansions on the outskirts of the city, in Juhu and Bandra.
This family of problems tends to a generalization of the classical maximum coverage problem as p goes to 0, and to a trivial instance of the knapsack problem as p goes to 1.
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Performance can be over-stated by comparing performance of NDS systems with trivial instances of traditional models.
"Even fleeting and seemingly trivial instances of interpersonal touch may help people to deal more effectively with existential concern," lead researcher Sander Koole wrote in the study.
Cross-pair-free instances of W-MTO are of special interest since they constitute our "trivial instances".
The idea is to identify a "trivial" (that is, polynomial-time solvable) special case of the problem and then to investigate instances that are close to these trivial instances, their closeness measured in terms of a certain parameter which is referred to as distance from triviality [ 19, 20].
We find already here a rich landscape of problems with non-trivial instances that are in P as well as those that are NP-complete.
There are many cones whose duals are trivial, for instance, see the following example.
If we are given malformed instances, we simply output a trivial NO-instance.
Our approach has been tested on a number of non-trivial synthetic instances and on a set of realistic industrial instances.
We consider two sets of non-trivial UFLP instances from UflLib [1] : ∘ mp-{1,2} and mq-{1,2} instances have been proposed by Kratica et al. [26].
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