L. HYAFIL AND R. L. RIVEST, Constructing optimal binary decision trees is NP-complete, Inform. Process. Lett., 5 (1976), pp. 15--17. Home/Search Document Not in Database Summary Related Articles Check |
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Optimal Depth-First Strategies for And-Or Trees - Greiner, Hayward, Molloy (2002) (Correct)
....to perform any tests, and so a 0 cost strategy is optimal. We can try to avoid this degeneracy by considering only positive formulae , where every variable occurs only positively. However, the MRSP remains NP hard here. Proof: reduction from ExactCoverBy3Set, using the same construction that [HR76] used to show the hardness of nding the smallest decision tree. A further restriction is to consider read once formulae, where each variable appears only one time. As noted above, we can view each such formula as an and or tree . The MRSP complexity here is not known. This paper considers ....
L. Hyal and R. Rivest. Constructing optimal binary decision trees is NP-complete. Information Processing Letters, 35(1):15--17, 1976.
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....subtrees within ceptable tolerances indeed the size of the tree before pruning may be strongly influenced by the node ordering used in the value tree. Again, this issue arises in research on classification [86, 112] Finding the smallest decision tree representing a given function is NP hard [60], but there are feasible heuristics one can use in our 82 Input: ranged value tree T Output: Labels SEQ LABEL indicating order in which to replace subtrees rooted at labelled node 1. Let SEQ = 1 2. Let F be the set of penultimate nodes in T (non leaf nodes all of whose children are leaves) ....
L. Hyafil and R. L. Rivest. Constructing optimal binary decision trees is NP-complete. Information Processing Letters, 5:15 17, 1976.
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....bounds on all projections is already comparable to O(k) distance calculations. The problem with tree structured implementations of hyperplanes, particularly k d trees, is that the construction of an optimal search tree for nearest neighbour searching has been found to be an NP complete problem [79]. On the other hand, using stationary hyperplanes in the trees, which is equivalent to using fixed bounds over the projection values, tends to fail to reduce the search volume whenever the target vector is close enough to the plane such that it is possible that there is a match better than the ....
L. Hyafil and R.L. Rivest. Constructing optimal binary decision trees is NP-complete. Information Processing Letters, 5(1):15--17, 1976.
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....optima. For instance inductive decision trees employ a greedy local optimization approach, and neural networks apply gradient descent techniques to minimize an error function over the training data. Moreover optimal training with finite data both for neural networks and decision trees is NP hard [13, 57]. As a consequence even if the learning algorithm can in principle find the best hypothesis, we actually may not be able to find it. Building an ensemble using, for instance, di#erent starting points may achieve a better approximation, even if no assurance of this is given. Another way to look at ....
L. Hyafil and R.L. Rivest. Constructing optimal binary decision tree is npcomplete. Information Processing Letters, 5(1):15--17, 1976.
Decision Trees: Equivalence and Propositional Operations - Zantema (1998) (Correct)
....criterion as in [8] yields the decision tree p(T ; T ) which is equivalent to the much smaller decision tree T . A usual objective, motivated by Occam s Razor, is trying to find a decision tree that is as small as possible. Finding the smallest tree consistent with some training set is NP hard ([6]) from this example we see that replacing the resulting tree by a smaller equivalent tree may already be helpful. In [3] an efficient algorithm is presented for this goal. Instead of elaborating this kind of practical applications, in this paper we concentrate on basic theoretical issues. We ....
Hyafil, L., and Rivest, R. L. Constructing optimal binary decision trees is NP-complete. Information Processing Letters 5, 1 (1976), 15--17.
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.... if (A[S] NONCONSTANT) then set D[S] 0; else set D [S] 1 min S(i) # D , D ### return D[# ] That f is given as a truth table is crucial: if f is non total and only the inputs for which f is defined are given, then deciding whether D(f) k for some k is NP complete [14]. 3.2. Certificate Complexity. Given an input X to f , a certificate for X is a constant valued restriction that agrees with X on the fixed variables. The size of the certificate is the number of fixed variables; note that querying these variables is su#cient to prove that f(X) 0 or f(X) 1, ....
L. Hyafil and R. L. Rivest, Constructing optimal binary decision trees is NP-complete, Information Proc. Lett., 5, pp. 15--17, 1976.
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Hya#l, L., & Rivest, R. L. #1976#. Constructing optimal binary decision trees is NPcomplete. Information Processing Letters, 5 #1#, 15#17.
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L. Hyafil and R. L. Rivest. Constructing optimal binary decision trees is NP-complete. Information Processing Letters, 5(1):15--17, 1976.
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Hyafil, L. and Rivest, R.L. (1976). Constructing optimal binary decision trees is NPcomplete. Information Processing Letters 5, 15--17.
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