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The College Application Problem

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Max Kapur, Sung-Pil Hong

Optimization and Control · Submitted 4 May 2022

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

The authors' main claim When colleges differ in their application fees, we show that the problem is NP-complete.

how it is stated · asserted 1.00 read the record →

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arXiv ID2205.01869 (version 2)
Pith ID4TGDFFJV, Pith's permanent record of this paper and its review
CitationMax Kapur, Sung-Pil Hong. "The College Application Problem." arXiv:2205.01869 (2022). https://pith.science/paper/4TGDFFJV
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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, 4,828 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.74 · human participants 0.04 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.27 · compares with prior results 0.11 · mentions code or data availability 0.03.

The abstract, sentence by sentence

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

This paper considers the maximization of the expected maximum value of a portfolio of random variables subject to a budget constraint. We refer to this as the optimal college application problem. When each variable's cost, or each college's application fee, is identical, we show that the optimal portfolios are nested in the budget constraint, yielding an exact polynomial-time algorithm. When colleges differ in their application fees, we show that the problem is NP-complete. We provide four algorithms for this more general setup: a branch-and-bound routine, a dynamic program that produces an exact solution in pseudopolynomial time, a different dynamic program that yields a fully polynomial-time approximation scheme, and a simulated-annealing heuristic. Numerical experiments demonstrate the algorithms' accuracy and efficiency.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 This paper considers the maximization of the expected maximum value of a portfolio of random variables subject to a budget constraint. contribution 0.55 0.37 0.06 asserted 0.82
s1 We refer to this as the optimal college application problem. contribution 0.55 0.55 0.04 asserted 0.89
s2 When each variable's cost, or each college's application fee, is identical, we show that the optimal portfolios are nested in the budget constraint, yielding an exact polynomial-time algorithm. result 0.98 0.95 0.17 asserted 1.00
s3 When colleges differ in their application fees, we show that the problem is NP-complete. result 0.99 0.94 0.22 asserted 1.00
s4 We provide four algorithms for this more general setup: a branch-and-bound routine, a dynamic program that produces an exact solution in pseudopolynomial time, a different dynamic program that yields a fully polynomial-time approximation scheme, and a simulated-annealing heuristic. method 0.55 0.95 0.13 asserted 1.00
s5 Numerical experiments demonstrate the algorithms' accuracy and efficiency. result 0.88 0.95 0.07 asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.56 · evidence from proof or derivation 0.96.

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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

This paper considers the maximization of the expected maximum value of a portfolio of random variables subject to a budget constraint. We refer to this as the optimal college application problem. When each variable's cost, or each college's application fee, is identical, we show that the optimal portfolios are nested in the budget constraint, yielding an exact polynomial-time algorithm. When colleges differ in their application fees, we show that the problem is NP-complete. We provide four algorithms for this more general setup: a branch-and-bound routine, a dynamic program that produces an exact solution in pseudopolynomial time, a different dynamic program that yields a fully polynomial-time approximation scheme, and a simulated-annealing heuristic. Numerical experiments demonstrate the algorithms' accuracy and efficiency.

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