Algorithmic problems

It approximates the expectation of the stochastic formulation (usually called the true problem) and can be solved using deterministic algorithms. Problem (9.19) can be solved iteratively in order to provide statistical bounds on the optimality gap of the objective function value. The iterative SAA procedure steps are explained in Section 7.5 of Chapter 7. 

The problems used proved very difficult for the students. They are clearly not straightforward algorithmic problems and have a number of features of true/realistic problems. One could even think of extremely difficult problems combining conceptual understanding and physicochemical calculations (727). 

The algorithmic problem treated here is given an (r, 3)-boundary, find all possible (r, 3)-fillings of it. 

DFG01] M. Deza, P. W. Fowler, and V. P. Grishukhin, Allowed boundary sequences for fused polycyclic patches, and related algorithmic problems, Journal of Chemical Information and Computer Science 41-2 (2001) 300-308. 

In putting everything together, we have to face these algorithmic problems (1) determine the optimal parameters 0 by maximizing the probability p(O,j 0) -this is a nonlinear global optimization problem-, (2) determine the optimal sequence of hidden metastable states j = jt) for given optimal parameters, and (3) determine the number of important metastable states which we, up to now, simply assumed to be identical with the number of hidden states. 

The length of the hidden Markov model is the number of match states. A profile HMM stands for a family of - in this case protein - sequences. Basically there are three algorithmic problems associated with an HMM. 

Computational correctness is mainly concerned with whether the algorithm has converged to the desired global minimum or to unintended local minima and explaining why this has happened. Also rounding-off error is important, as is reproducibility of the calculations. These are algorithmic problems. For a data analyst such aspects should ideally not be of concern, but unfortunately, some three-way models are not numerically simple to fit. 

Nakhleh, M.B. (1993). Are our students conceptual thinkers or algorithmic problem solvers Journal of Chemical Education, 70, 52-55. 

Actually, a classification of problems is needed for further clarification. On the one hand, thdfe are data-processing problems, where the specification is almost tantamount to an actual program. On the other hand, there are algorithmic problems, where the specification is at best some kind of a naive (inefficient) program. The focus in this... 

Such a methodology has been formulated. It aims at programming-in-the-small, and is (mainly) meant for algorithmic problems. It is sub-divided into three stages ... 

Once an axiom is known, however, then the computation of halters and nonhalters for which sufficient axioms are known becomes an algorithmic problem. Therefore, the discovery of new axioms converts subsets of problems from non-algorithmic... 

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