By the same authors

Distance Metric Ensemble Learning and the Andrews-Curtis Conjecture

Research output: Other contribution

Standard

Distance Metric Ensemble Learning and the Andrews-Curtis Conjecture. / Krawiec, Krzysztof; Swan, Jerry.

11 p. 2016.

Research output: Other contribution

Harvard

Krawiec, K & Swan, J 2016, Distance Metric Ensemble Learning and the Andrews-Curtis Conjecture.. <http://arxiv.org/abs/1606.01412>

APA

Krawiec, K., & Swan, J. (2016). Distance Metric Ensemble Learning and the Andrews-Curtis Conjecture. http://arxiv.org/abs/1606.01412

Vancouver

Krawiec K, Swan J. Distance Metric Ensemble Learning and the Andrews-Curtis Conjecture. 2016. 11 p.

Author

Krawiec, Krzysztof ; Swan, Jerry. / Distance Metric Ensemble Learning and the Andrews-Curtis Conjecture. 2016. 11 p.

Bibtex - Download

@misc{e96937f587394919924933630acde4e3,
title = "Distance Metric Ensemble Learning and the Andrews-Curtis Conjecture",
abstract = "Motivated by the search for a counterexample to the Poincar{\'e} conjecture in three and four dimensions, the Andrews-Curtis conjecture was proposed in 1965. It is now generally suspected that the Andrews-Curtis conjecture is false, but small potential counterexamples are not so numerous, and previous work has attempted to eliminate some via combinatorial search. Progress has however been limited, with the most successful approach (breadth-first-search using secondary storage) being neither scalable nor heuristically-informed. A previous empirical analysis of problem structure examined several heuristic measures of search progress and determined that none of them provided any useful guidance for search. In this article, we induce new quality measures directly from the problem structure and combine them to produce a more effective search driver via ensemble machine learning. By this means, we eliminate 19 potential counterexamples, the status of which had been unknown for some years.",
author = "Krzysztof Krawiec and Jerry Swan",
year = "2016",
language = "English",
type = "Other",

}

RIS (suitable for import to EndNote) - Download

TY - GEN

T1 - Distance Metric Ensemble Learning and the Andrews-Curtis Conjecture

AU - Krawiec, Krzysztof

AU - Swan, Jerry

PY - 2016

Y1 - 2016

N2 - Motivated by the search for a counterexample to the Poincaré conjecture in three and four dimensions, the Andrews-Curtis conjecture was proposed in 1965. It is now generally suspected that the Andrews-Curtis conjecture is false, but small potential counterexamples are not so numerous, and previous work has attempted to eliminate some via combinatorial search. Progress has however been limited, with the most successful approach (breadth-first-search using secondary storage) being neither scalable nor heuristically-informed. A previous empirical analysis of problem structure examined several heuristic measures of search progress and determined that none of them provided any useful guidance for search. In this article, we induce new quality measures directly from the problem structure and combine them to produce a more effective search driver via ensemble machine learning. By this means, we eliminate 19 potential counterexamples, the status of which had been unknown for some years.

AB - Motivated by the search for a counterexample to the Poincaré conjecture in three and four dimensions, the Andrews-Curtis conjecture was proposed in 1965. It is now generally suspected that the Andrews-Curtis conjecture is false, but small potential counterexamples are not so numerous, and previous work has attempted to eliminate some via combinatorial search. Progress has however been limited, with the most successful approach (breadth-first-search using secondary storage) being neither scalable nor heuristically-informed. A previous empirical analysis of problem structure examined several heuristic measures of search progress and determined that none of them provided any useful guidance for search. In this article, we induce new quality measures directly from the problem structure and combine them to produce a more effective search driver via ensemble machine learning. By this means, we eliminate 19 potential counterexamples, the status of which had been unknown for some years.

M3 - Other contribution

ER -