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Questions tagged [trees]

Questions about a special kind of graphs, namely connected and cycle-free ones.

166 questions with no upvoted or accepted answers
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38
votes
0answers
1k views

Is there a regular tree language in which the average height of a tree of size $n$ is neither $\Theta(n)$ nor $\Theta(\sqrt{n})$?

We define a regular tree language as in the book TATA: It is the set of trees accepted by a non-deterministic finite tree automaton (Chapter 1) or, equivalently, the set of trees generated by a ...
18
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1answer
745 views

Why hasn't functional programming researched dynamic trees?

Dynamic trees play an important role in solving problems such as network flows, dynamic graphs, combinatorial problems ("Dynamic Trees in Practice" by Tarjan and Werneck) and recently merging ...
16
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0answers
334 views

Is finding a weight-balanced tree NP-hard?

In the following, we consider binary trees where only the leaves have weights. Let $T$ be a binary tree and $W(T)$ be the sum of the weights of its leaves. Let $T.l$ and $T.r$ be the left child and ...
8
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0answers
145 views

What is the best algorithm to compute ALL homomorphisms between two rooted labeled trees?

Lets consider two node-labeled rooted trees Q and D. According to wikipedia definition ( https://en.wikipedia.org/wiki/Tree_homomorphism ) a mapping m from the nodes of Q to the nodes of D is a tree ...
5
votes
1answer
353 views

What is the minimum required storage for a sparse, depth-first octree?

For a numerical simulation framework, I use a hierarchical Cartesian grid in 3D to discretize the computational domain. I am thus looking for the most space-efficient way to store the resulting octree ...
5
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0answers
138 views

Assignment of coprime values to a tree

I recently saw this question somewhere and thought a lot on it but was unable to find an efficient solution for it. Asked on Stack Overflow but got no solution there. The Problem is as follows - ...
5
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0answers
129 views

Has this graph-theoretic problem got a known name? Is it NP-hard?

I am considering the following problem. We are given a Directed Acyclic Graph. In general, there would be some number of subgraphs that, contracted into one node, would make it a tree. For example, ...
5
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0answers
289 views

Understanding the Baeza-Yates Régnier algorithm (multiple string matching, extended from Boyer-Moore)

First of all, excuse me if I write a lot, I tried to summarize my research so that everyone can understand. R. Baeza-Yates and M. Regnier published in 1993 a new algorithm for searching a two ...
4
votes
1answer
43 views

How to find all the edges shared by all diametral paths of a tree?

A diametral path in a graph is a shortest path whose length is equal to the diameter of the graph. Now, given a tree with $n$ nodes, I would like to find the set of edges (possibly empty) which are ...
4
votes
1answer
47 views

How do 2-3 FingerTrees generalize to bigger branching factors?

FingerTrees as implemented by Haskell's Data.Sequence use a branching factor of 2-3 for Nodes, and have Digits of size 1-4. Imagine we want to make the branching factor much wider -- perhaps to ...
4
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0answers
56 views

Repeated nearest-neighbor queries

If I want to make N repeated (i.e. millions of) 2D nearest-neighbor queries on a pointset of size M, is traveling down into a KD-Tree most efficient or are there better ways to do this? (e.g. Voronoi?)...
4
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0answers
156 views

Weak equivalent tree grammar for Context-sensitive word grammar?

Consider arbitrary context-sensitive grammar on strings $G_s$. Is any known and described formalism (or type) for tree grammars, using which we can build weak-equivalent tree grammar $G_t$, which ...
4
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0answers
140 views

Data structure for a Rete in production rule system

Example of Data This is the data for one monkey. There are many similar but different monkeys. ...
4
votes
0answers
2k views

Maximizing pruned branches in an alpha-beta tree

Preliminary After doing some searches of similar questions posted here and elsewhere, i feel like this is the right place to inquire about, now let's get through some boring main notations... A ...
4
votes
0answers
140 views

MST that contains a shortest $s,t$-path

Consider the problem in which we have an (undirected) graph $G=(V,E)$, weight function $w:E\to\mathbb N$ and a pair of vertices $s,t\in V$, and are required to determine whether there exists an MST $T$...
4
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0answers
235 views

Minimal Steiner Tree in unweighted directed graph

I have an unweighted directed graph $(V, E)$ and a subset $T \subseteq V$ of these vertices. I want to find the minimum tree $(V',E')$ that contains all these $T$ vertices (minimize in number of nodes ...
4
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0answers
541 views

Why does a first-child-next-sibling tree implementation have parent pointers?

Below is the code, ...
3
votes
1answer
56 views

What is a polynomial-time algorithm for determining whether two trees, with colored nodes, are isomorphic or not

Provide any polynomial-time algorithm (even a large degree polynomial) which determines whether two rooted colored trees are isomorphic to each-other or not. For example, consider the following two ...
3
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0answers
39 views

Tree Automata Operators

I am trying to understand the Projection operation (linear tree homomorphism) and Cylindrification operation (inverse tree homomorphism) from the book. Linear Tree homomorphism is defined as follows: ...
3
votes
1answer
131 views

minimum and maximum nodes of MultiWay tree of height h

I know that it doesn’t have to be balanced so in theory given that the height of the tree is $h$, the minimal number of nodes is obtained when each node has 1 key and 1 child, and since the first ...
3
votes
0answers
451 views

How can we describe the similarity between trees?

For example, I have a program generates two ASTs, and I want to compare the two trees. I've tried to treat the trees as graphs, but I think it doesn't show the particularity of trees.
3
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0answers
968 views

Lowest single common ancestor in a Directed Acyclic Graph?

I was reading how to find the Lowest common ancestor in a DAG. A DAG can have scenarios where the LCA yields multiple solutions and I feel the accepted answer explains that pretty well. However, one ...
3
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0answers
376 views

B+tree implementation using single file on disk

I'm studying B+trees and I'm trying to understand how actual data can be stored in a physical file and still allow fast lookups. None of it would be in memory, all of the pointers would be "seeks" to ...
3
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0answers
1k views

What is the Big-Oh asymptotic complexity of learning in Random Forests?

Random Forests is a bagged ensemble of CART learners. The following is what I've found, but am not sure if I'm completely right. CART (Classification and Regression Trees) uses the Gini index for ...
3
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0answers
760 views

Tree of Despair: Collecting Data from a Tree with Multiple Types of Branching

Provided is a tree with three types of node. The structure of the tree cannot be modified and traversal of the tree is limited to querying a node for its children or its parent. The objective of the ...
3
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0answers
74 views

What is the intuition behind the “edit sensitive parsing” tree?

If I understand right then ESP tree is defined as : given any string $x$ of finite length over an alphabet one can construct "an" ESP tree corresponding to it say $T_x$ such that each leaf of the tree ...
3
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0answers
194 views

How to apply path compression to Multi-Bit Trie

Reading a bit about the subject of Multi-Bit tries and IP matching in: High Performance Switches and Routers H. Jonathan Chao, Bin Liu. Page 33 Network Routing: Algorithms, Protocols, and ...
3
votes
1answer
664 views

what is the name for the space between the leaves of a tree

I am trying to write a data-type not for a tree, but for the spaces in between the leaves of thee tree. In number theory (a part of math) this is known as a topograph does it have a name in CS?
2
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0answers
94 views

How to query the tree?

I encountered an interesting problem based on tree-data-structure. We are given a tree which has N nodes, with 1≤N≤105. Time starts from second 1 and it continues for q seconds. At each ...
2
votes
0answers
43 views

How to solve following tree problem?

Source of the problem is https://codeforces.com/contest/1152/problem/D . I think i understood the problem , but if possible please explain the problem in simple way and the solution also .I tried very ...
2
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0answers
18 views

Nested dissection vs kd-tree

Could you explain, please, the difference between the nested dissection and kd-tree. For me they look same representing a tree data structure for a distribution of points in a multi-dimensional ...
2
votes
0answers
100 views

Join Order Optimization

Consider the join: (σtitle=Overwatch Game)⨝ Event ⨝ rating ⨝ Player What is the optimal join order? Based on the schema on the following picture: I am suppoused (and that's what I tried) to use ...
2
votes
0answers
29 views

Construct a lambda term from a Böhm tree

Given an acyclic graph, how can I build a lambda calculus term such that this graph is the term's Böhm tree? If the Böhm tree is a finite tree (so the result is a strongly normalizing term). If the ...
2
votes
0answers
35 views

Documentation of “bin number” trees

TL;DR: I implemented a special (?) binary tree and can't find any further details on the method I used on the internet. I would like to know if there are any scientific papers discussing my ...
2
votes
0answers
122 views

Algorithm to find nodes with given a distance

We have a map of a branching river without any islands (tree of confluences, see picture), there are piers on the river bank ( not necessarily on the confluences). We are given the distances between ...
2
votes
0answers
210 views

Semi-automatic layout algorithms for a mind map

There're some existing tree layout algorithms such as Tidier Drawings of Trees and Drawing Non-layered Tidy Trees in Linear Time. I call them as automatic layout algorithms since positions of nodes ...
2
votes
0answers
153 views

K-ary tree that wrapped around

I'm not sure the best way to name this problem, but basically I need to construct a complete $k$-ary tree for $k \geq 2$ which has this nice property as $k=1$ tree that we can create a ring out of it. ...
2
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0answers
68 views

stacks in tree constructions

There are two nice tree constructions, that use a stack in a similar manner: Construct a binary search tree from a pre-order traversal (e.g. see http://www.geeksforgeeks.org/construct-bst-from-given-...
2
votes
0answers
73 views

How to cut a full binary tree evenly

Given a full binary tree of size $n$, I need to cut the tree into two by choosing an edge and removing it. I want the cutting to be as equal as possible (i.e. the two subtrees have as equal weight as ...
2
votes
0answers
18 views

How to avoid empty spots when inserting in a B+tree

When you insert a new item in a B+tree leaf node, and the node is full, two new nodes are created and they're both filled halfway and the values get re-distributed accordingly. Before the insertion: ...
2
votes
0answers
111 views

Coloring of a K-ary tree using minimum paint Buckets

I was recently asked this problem in an interview and I couldn't solve it. Need some help on how to solve this problem. Given a K-ary tree with N nodes (N <= 2000 and K <= 12) you need to ...
2
votes
0answers
88 views

Counting inversions with index constraint

I have a series of line segments $l_i=(a_i,b_i)$ with $i=1,2,3...n$ $a_i$ and $b_i$ are their starting and ending points coordinates in $x$ axis. The question is how to find a algorithm that is ...
2
votes
0answers
467 views

Minimum cost edge in path between nodes (tree)

I'm working on a problem and I've managed to design an efficient algorithm, but I'm stuck at the last part. After some processing I'm left with a tree and I have to answer several queries of the ...
2
votes
1answer
574 views

How to efficiently create balanced KD-Trees from a static set of points

From Wikipedia, KD-Trees: Alternative algorithms for building a balanced k-d tree presort the data prior to building the tree. They then maintain the order of the presort during tree construction ...
2
votes
0answers
54 views

Two flavors of red-black trees with different performance

I've implemented two red-black trees (using the pseudo-code in CLRS) with slightly different flavors: 1) In the first tree, all the data is stored in the leaves. 2) In the second tree, the data is ...
2
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0answers
72 views

Which component sizes do we observe while randomly deconstructing a tree?

Suppose I have a connected graph with $n$ vertices and $n−1$ edges, that is in form of a tree. Now, I will add the number of vertices in the tree and uniformly randomly select a vertex. I break the ...
1
vote
0answers
39 views

Data structure for storing strings

I'm designing a tree data structure to store strings in. One classic solution is prefix tree, but I am looking for a solution that the time to check if the string is in the storage is O(logm*logn) ...
1
vote
0answers
10 views

Minimum Weight Binary Spanning Tree

Let $G=(V,E)$ be a simple graph with weights $w_{ij}$ (can be assumed to be positive). Is it possible to find the minimum (or maximum) weight, rooted spanning tree that is binary? That means every ...
1
vote
0answers
17 views

Directed Trees: Finding all the edges and vertices in a specific direction

I am an electrical engineer without experience in graph theory. However, I have a problem which I believe can be solved by graph theory. We have a directed tree, such as the one below. We want to find ...
1
vote
1answer
62 views

Minimum distance of nodes from a set of two nodes

In an unweighted tree, suppose that we want to delete (or mark) any node which is closer to node $v$ than node $w$ ($dist(x,v) < dist(x,w)$). The solution that comes to my mind is running two BFS, ...