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But the major reason is to understand how to cope with full history dependence in a (deceptively easy-looking) problem. On the Ester's Book International Conference in Israel (2006) Robbins' problem was accordingly named one of the four most important problems in the field of optimal stopping and sequential analysis.
When the research is complete and the researcher knows the (probable) answer to the research question, writing up can begin (as distinct from writing notes, which is a process that goes on through a research project). In term papers, the answer to the question is normally given in summary in the introduction in the form of a thesis statement.
The quadratic assignment problem (QAP) is one of the fundamental combinatorial optimization problems in the branch of optimization or operations research in mathematics, from the category of the facilities location problems first introduced by Koopmans and Beckmann. [1] The problem models the following real-life problem:
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Problem discovery is an unconscious process which depends upon knowledge whereby an idea enters one's conscious awareness, problem formulation is the discovery of a goal; problem construction involves modifying a known problem or goal to another one; problem identification represents a problem that exists in reality but needs to be discovered ...
[2] [3] An important open mathematics problem solved in the early 21st century is the Poincaré conjecture. Open problems exist in all scientific fields. For example, one of the most important open problems in biochemistry is the protein structure prediction problem [4] [5] – how to predict a protein's structure from its sequence.
Although an understanding of the complete system is usually considered necessary for good design—leading theoretically to a top-down approach—most software projects attempt to make use of existing code to some degree. Pre-existing modules give designs a bottom-up flavor.
Establishing whether a constraint satisfaction problem on a finite domain has solutions is an NP-complete problem in general. This is an easy consequence of a number of other NP-complete problems being expressible as constraint satisfaction problems. Such other problems include propositional satisfiability and three-colorability.