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Decision trees are often employed to understand algorithms for sorting and other similar problems; this was first done by Ford and Johnson. [1]For example, many sorting algorithms are comparison sorts, which means that they only gain information about an input sequence ,, …, via local comparisons: testing whether <, =, or >.
Decision trees, influence diagrams, utility functions, and other decision analysis tools and methods are taught to undergraduate students in schools of business, health economics, and public health, and are examples of operations research or management science methods. These tools are also used to predict decisions of householders in normal and ...
The problem of learning an optimal decision tree is known to be NP-complete under several aspects of optimality and even for simple concepts. [35] [36] Consequently, practical decision-tree learning algorithms are based on heuristics such as the greedy algorithm where locally optimal decisions are made at each node. Such algorithms cannot ...
For example, a greedy strategy for the travelling salesman problem (which is of high computational complexity) is the following heuristic: "At each step of the journey, visit the nearest unvisited city." This heuristic does not intend to find the best solution, but it terminates in a reasonable number of steps; finding an optimal solution to ...
A notable problem occurs when information gain is applied to attributes that can take on a large number of distinct values. For example, suppose that one is building a decision tree for some data describing the customers of a business.
In contrast, decision trees count each decision as a single step. Dobkin and Lipton [13] show an lower bound on linear decision trees for the knapsack problem, that is, trees where decision nodes test the sign of affine functions. [14] This was generalized to algebraic decision trees by Steele and Yao. [15]
C4.5 is an algorithm used to generate a decision tree developed by Ross Quinlan. [1] C4.5 is an extension of Quinlan's earlier ID3 algorithm.The decision trees generated by C4.5 can be used for classification, and for this reason, C4.5 is often referred to as a statistical classifier.
NP-complete special cases include the edge dominating set problem, i.e., the dominating set problem in line graphs. NP-complete variants include the connected dominating set problem and the maximum leaf spanning tree problem. [3]: ND2 Feedback vertex set [2] [3]: GT7 Feedback arc set [2] [3]: GT8 Graph coloring [2] [3]: GT4