Questions tagged [decision-trees]

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Is it possible that the Aanderaa–Karp–Rosenberg conjecture is just a bit false?

The Aanderaa–Karp–Rosenberg conjecture is that any non-trivial monotone property on graphs is evasive. It has been proved for several special cases, but for a general graph on $n$ vertices, we only ...
337 views

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 ...
125 views

Finding the maximum no. of people who get along in a group [closed]

Suppose that there are 15 people in a room. Assume that each person gets along with other people in the room (but not everyone). (Note that the "feeling is mutual" between any two people who are ...
139 views

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", ...
251 views

Algebraic decision trees and adversary arguments

In the comparison tree model, we establish lower bounds on computing $\min$ and $\max$ of $n$ numbers via the adversary argument. Are there problems on which we know lower bounds in the algebraic ...
782 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 $2$-...
509 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 ...
186 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 ...
583 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 ...
150 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 ...
598 views

Canonical representation of Binary Decision Tree in Ptime?

I am wondering whether there may exist a way to give a sort of "normal form" for binary decision trees (BDT) in a tractable way. More precisely: a BDT is a tree with internal nodes labelled by ...
833 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 ...
169 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 ...
379 views

Lower bound for finding repeated elements in sorted array

This is inspired by  (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 ...
308 views

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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 $\{1,\ldots,d-1\}$ ...
431 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 ...
579 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. ...
616 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 ...
154 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 ...
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 ...
2k views

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 ...
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? ...
585 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 ...
300 views

Sorting : proof for lower bound of Sorting [closed]

I have read the proof of lower bound of Sorting Algorithm that use comparison to know input is NlogN. In this paper, the author use decision tree for this proof. Everything on this proof I have ...
236 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 $T'$ ...
238 views

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 ...
94 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,...
724 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 ...
Consider a boolean function $f : V \rightarrow \{0,1\}$ with $m$ true points. Are there any non-trivial bounds in $m$ on the size of the smallest decision tree for $f$? It seems to me that assuming \$...