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Bibliographic Details

Title

On the Complexity of Four Polyhedral Set Containment Problems (Classic Reprint)

Publisher

Forgotten Books

Publication Date

2024

Language

English

ISBN 10

0365899887

ISBN 13

9780365899884

Binding

Paperback

Condition

New

Book Type

print-on-demand item

Seller catalogs

Calculus

About this title

Synopsis

Exploring why some polyhedral containment problems defy easy answers.

This work examines how certain seemingly straightforward questions about placing one polyhedron inside another fall into the hard, NP-complete camp, shaping our understanding of computational limits in geometry and optimization.

The discussion centers on three set containment problems, each formed by X and Y as special polyhedral or ball-like shapes. It also looks at the related integer containment problem and the complexity of finding integer points inside polyhedra. Readers will see how classical reductions connect these geometric questions to well-known hard problems, and how polynomial-time solvability in some cases does not extend to all.

The problems examined include HB, HW, and BW, which ask whether one set is contained in another under different geometric constraints.
The work shows these three problems are NP-complete, strengthening the view that some polyhedral containment tasks resist efficient solutions.
It presents a chain of reductions from the 0-1 knapsack problem and the integer containment problem, illustrating why certain forms become intractable.
It also discusses ICP2, the problem of finding an integer point in a polyhedron, and establishes its NP-completeness.

Ideal for readers of computational geometry, optimization theory, and researchers exploring the boundaries between tractable and intractable problems in linear and integer programming.

"About this title" may belong to another edition of this title.

Store Description

Forgotten Books? Classic Reprint Series utilizes the latest technology to regenerate facsimiles of historically important writings. Careful attention has been made to accurately preserve the original format of each page whilst digitally enhancing the quality of the aged text.

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