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# Questions tagged [decision-trees]

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### Coloring complexity of graphs

Suppose $G$ is a graph with coloring number $d = \chi(G)$. Consider the following game between Alice and Bob. At each round, Alice picks a vertex, and Bob answers with a color in $\{1,\ldots,d-1\}$ ...
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642 views

### The randomized query complexity of the conjoined trees problem

An important 2003 paper by Childs et al. introduced the "conjoined trees problem": a problem admitting an exponential quantum speedup that's unlike just about any other such problem that we know of. ...
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848 views

### Easy problems with hard counting versions

Wikipedia provides examples of problems where the counting version is hard, whereas the decision version is easy. Some of these are counting perfect matchings, counting the number of solutions to $2$-...
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2k views

### Sorting using a black box

Assume that we want to sort a list $S$ of $n$ real numbers. Assume that we are given a black box that can sort $\sqrt n$ real numbers instantly. How much advantage can we gain using this black box? ...
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### Algorithm for optimizing decision trees

Background A binary decision tree $T$ is a rooted tree where each internal node (and root) is labeled by an index $j \in \{1,..., n\}$ such that no path from root to leaf repeats an index, the leafs ...
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649 views

### Provable gaps between decision tree complexity and "true" complexity

The title is a little misleading: but hopefully the question isn't: Grønlund and Pettie's new result showing that 3SUM has only $O(n^{3/2})$ decision tree complexity got me wondering: Is there a ...
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884 views

### Las Vegas vs Monte Carlo randomized decision tree complexity

Background: Decision tree complexity or query complexity is a simple model of computation defined as follows. Let $f:\{0,1\}^n\to \{0,1\}$ be a Boolean function. The deterministic query complexity of ...
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447 views

### How can one find the "hard" probability distribution on the input for recursive boolean functions?

Update: Since, it seems there is no progress regarding this question, any idea, conjecture, hunch, or advice is welcome. For example, are there any partial or incomplete results? What are the main ...
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### Complexity of constructing minimum depth decision trees

I am interested in the computational complexity of Problem 1: Given a finite, non-empty set $J$, given $A, B \subseteq \{0,1\}^J$ such that $A \cap B = \emptyset$, and given $n \in \mathbb{N}$, does ...
• 193
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### Is there an accepted name for Ross Quinlan's adaptation of the ID3 decision algorithm to use a Pearson's chi-squared test for independence?

In Ross Quinlan's seminal paper Induction of Decision Trees, Quinlan summarizes the current state of machine learning in 1985 and loudly introduces the ID3 decision algorithm in the context of its ...
• 163
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### Generalization of the generalization of the evasiveness conjecture

The generalized evasiveness conjecture (Aanderaa, Rosenberg, Karp, Kahn, Saks, Sturtevant) states that any non-constant, monotone ($x\le y \Rightarrow f(x)\le f(y)$, weakly symmetric Boolean function ...
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283 views

### Tree rotation, a problem similar to Huffman coding

I am not sure whether the following problem has been studied. We have a undirected tree $T$. We would like to construct another tree $T'$. $T'$ is a binary tree. Each inner nodes of $T'$ ...
• 769
188 views

### Lower bound for sorting without using a decision tree model

Can we prove the lower bound for the sorting problem just by Turing machine model? It seems that available proof of sorting is based on the assumption that the algorithm only uses comparison so we can ...
881 views

### Building a decision tree to approximate a known function (not to learn an unknown function)

I have a function $f: \mathbb{D} \rightarrow \{0,1\}$ where $\mathbb{D} \in \mathbb{R}^{5000}$. I would like to approximate $f$ using a decision tree. Up to now I have only found literature in the ...
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74 views

### Hardness of Computing Tribes-DNF by Decision Trees

In this paper on "The Polynomial Hierarchy, Random Oracles, and Boolean Circuits", Fact (3.2) states that it is impossible for a polylogarithmic depth decision tree to compute the Tribes-DNF ...
• 51
175 views

### The Complexity of Properly Learning Decision Trees

Where does this paper prove the middle bullet point of its abstract? I have looked through that paper fairly thoroughly. There are three things I want to read how they're getting around. Reductions ...
566 views

### Lower bound on the element distinctness problem

The element distinctness problem asks whether any two elements of the input sequence $<x_1,\ldots,x_n>$ are equal? This problem has a lower bound of $\Omega(n \log n)$ in the algebraic decision ...
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### Approximation class of finding decision trees with minimal depth

We are given some sets $S_1, \cdots , S_n$ and two disjoint sets $A$ and $B$. A decision tree is a binary tree where each node asks "$x \in S_i?$" for some $i$, taking the left branch means "yes", ...
696 views

### Is there a tight lower bound on the complexity of SSSP on a graph?

I'm an undergrad and I'm not sure if this is the right way to ask this question. I want to know the lower bound on single-source shortest path computation in a general graph. The graph is allowed to ...
452 views

### Lower bound for finding repeated elements in sorted array

This is inspired by [1] (which still needs answers). What is the tight lower bound (or optimal algorithms) for the "finding repeated elements" problem: Given a sorted integer array of size $n$, how ...
• 2,329
48 views

### Learning a boolean function using decision tree with small number of queries

I am working on a problem and I am looking to solve the following subproblem : Given a "restrictive" blackbox access to boolean function $\phi$, output a "small-sized" CNF that ...
157 views

### How hard is it to compute an approximately optimal non-greedy CART tree?

The question itself is closer to the bottom of this post, and is formulated without any rerefence to the term "CART". Motivation: In traditional CART (Classification and Regression Trees), one ...
1 vote
704 views

### Minmax vs Maxmin

I'm reading this paper about building a combat simulator for 8 unit vs 8 unit mini combats in StarCraft: Brood War. The basic idea is to build a search tree simulating these small combats in order to ...
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1 vote
159 views

### decision tree complexity and query complexity

I want good sources for starting with decision tree complexity and query complexity , what papers to start with ? what book chapters to read ? I already seen arora and barak book and I begin to read ...
1 vote
178 views

### If boolean function $f$ is computable by a k-CNF and an l-DNF then it can be computed by a decision tree of depth at most kl

I have seen it stated that if boolean function $f$ is computable by a $k$-CNF and an $l$-DNF then it can be computed by a decision tree of depth at most $kl$. However, I am not able to see why this is ...
1 vote
215 views

### Randomized and deterministic query complexity of symmetric functions

The deterministic query complexity $D(f)$ of a symmetric function $f$ is $\Omega(n)$ (except for f = 0 or f = 1). I am wondering if the same result holds for the (bounded-error) randomized query ...
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### Learning using decision trees

I have a quick question that I'm stumped on. This is about constructing a decision tree using information gain (entropy). Let's say we have a dataset with two input attributes such that the ...
96 views

### Designing an appropriate training set for CART classification using imbalanced data

I'm experimenting with using CART (or maybe Random Forest) to classify genomic data. There are essentially two classes, whereof one is the 'normal' state and the other is the 'exceptional' state. Now,...
2k views

### Time complexity analysis of random forest and k-means?

I am working with random forest for a supervised classification problem, and I am using the k-means clustering algorithm to split the data at each node, where $n$ is the number of points, $K$ is ...