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Chapter 8. Fundaments of Branching Heuristics

Oliver Kullmann Orcid Logo

Frontiers in Artificial Intelligence and Applications, Volume: 336

Swansea University Author: Oliver Kullmann Orcid Logo

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DOI (Published version): 10.3233/faia200991

Abstract

“Search trees”, “branching trees”, “backtracking trees” or “enumeration trees” are at the heart of many (complete) approaches towards hard combinatorial problems, constraint problems, and, of course, SAT problems. Given many choices for branching, the fundamental question is how to guide the choices...

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Published in: Frontiers in Artificial Intelligence and Applications
ISSN: 0922-6389 1879-8314
Published: IOS Press 2021
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URI: https://cronfa.swan.ac.uk/Record/cronfa70993
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last_indexed 2026-01-16T05:32:54Z
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spelling 2026-01-15T20:16:16.5734830 v2 70993 2025-11-26 Chapter 8. Fundaments of Branching Heuristics 2b410f26f9324d6b06c2b98f67362d05 0000-0003-3021-0095 Oliver Kullmann Oliver Kullmann true false 2025-11-26 MACS “Search trees”, “branching trees”, “backtracking trees” or “enumeration trees” are at the heart of many (complete) approaches towards hard combinatorial problems, constraint problems, and, of course, SAT problems. Given many choices for branching, the fundamental question is how to guide the choices so that the resulting trees are (relatively) small. Despite (or perhaps because) of its apparently more narrow scope, especially in the SAT area several approaches from theory and applications have found together, and the rudiments of a theory of branching heuristics emerged. In this chapter the first systematic treatment is given. So a general theory of heuristics guiding the construction of “branching trees” is developed, ranging from a general theoretical analysis to the analysis of the historical development of branching heuristics for SAT solvers, and also to heuristics beyond SAT solving. Journal Article Frontiers in Artificial Intelligence and Applications 336 IOS Press 0922-6389 1879-8314 31 12 2021 2021-12-31 10.3233/faia200991 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University Not Required 2026-01-15T20:16:16.5734830 2025-11-26T10:49:16.8852852 Faculty of Science and Engineering School of Mathematics and Computer Science - Computer Science Oliver Kullmann 0000-0003-3021-0095 1
title Chapter 8. Fundaments of Branching Heuristics
spellingShingle Chapter 8. Fundaments of Branching Heuristics
Oliver Kullmann
title_short Chapter 8. Fundaments of Branching Heuristics
title_full Chapter 8. Fundaments of Branching Heuristics
title_fullStr Chapter 8. Fundaments of Branching Heuristics
title_full_unstemmed Chapter 8. Fundaments of Branching Heuristics
title_sort Chapter 8. Fundaments of Branching Heuristics
author_id_str_mv 2b410f26f9324d6b06c2b98f67362d05
author_id_fullname_str_mv 2b410f26f9324d6b06c2b98f67362d05_***_Oliver Kullmann
author Oliver Kullmann
author2 Oliver Kullmann
format Journal article
container_title Frontiers in Artificial Intelligence and Applications
container_volume 336
publishDate 2021
institution Swansea University
issn 0922-6389
1879-8314
doi_str_mv 10.3233/faia200991
publisher IOS Press
college_str Faculty of Science and Engineering
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hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Computer Science{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Computer Science
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description “Search trees”, “branching trees”, “backtracking trees” or “enumeration trees” are at the heart of many (complete) approaches towards hard combinatorial problems, constraint problems, and, of course, SAT problems. Given many choices for branching, the fundamental question is how to guide the choices so that the resulting trees are (relatively) small. Despite (or perhaps because) of its apparently more narrow scope, especially in the SAT area several approaches from theory and applications have found together, and the rudiments of a theory of branching heuristics emerged. In this chapter the first systematic treatment is given. So a general theory of heuristics guiding the construction of “branching trees” is developed, ranging from a general theoretical analysis to the analysis of the historical development of branching heuristics for SAT solvers, and also to heuristics beyond SAT solving.
published_date 2021-12-31T05:34:09Z
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