A Simple Solution to the Level-Ancestor Problem

Dhruv Matani; Gaurav Menghani

RECORD

A Simple Solution to the Level-Ancestor Problem

Gaurav Menghani, Dhruv Matani

Data Structures and Algorithms · Submitted 4 Mar 2019

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We present a simple solution, which pre-processes the tree in $O(n)$ time with $O(n)$ extra space, and answers the queries in $O(\log\ {n})$ time.

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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,935 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.49 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.86 · mentions code or data availability 0.03.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

A Level Ancestory query LA($u$, $d$) asks for the the ancestor of the node $u$ at a depth $d$. We present a simple solution, which pre-processes the tree in $O(n)$ time with $O(n)$ extra space, and answers the queries in $O(\log\ {n})$ time. Though other optimal algorithms exist, this is a simple enough solution that could be taught and implemented easily.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	A Level Ancestory query LA($u$, $d$) asks for the the ancestor of the node $u$ at a depth $d$.	background 1.00	0.07	0.04	asserted 0.99
s1	We present a simple solution, which pre-processes the tree in $O(n)$ time with $O(n)$ extra space, and answers the queries in $O(\log\ {n})$ time.	contribution 0.82	0.95	0.78	asserted 1.00
s2	Though other optimal algorithms exist, this is a simple enough solution that could be taught and implemented easily.	interpretation 0.87	0.25	0.19	hedged possibility 0.89

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from proof or derivation 0.84.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

A Level Ancestory query LA($u$, $d$) asks for the the ancestor of the node $u$ at a depth $d$. We present a simple solution, which pre-processes the tree in $O(n)$ time with $O(n)$ extra space, and answers the queries in $O(\log\ {n})$ time. Though other optimal algorithms exist, this is a simple enough solution that could be taught and implemented easily.

Human review

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How the literature uses it

1 arXiv paper cite this in 2 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it

Cites it as background 1 paper

Several sequential and parallel algorithms are known for this problem [ref] .

Simpler O(1) Query Algorithm for Level Ancestors · Introduction · 1.00

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