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Record W2141507454

Multi-guard covers for polygonal regions

2010· article· en· W2141507454 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

VenueCanadian Conference on Computational Geometry · 2010
Typearticle
Languageen
FieldComputer Science
TopicComputational Geometry and Mesh Generation
Canadian institutionsUniversity of British Columbia
Fundersnot available
KeywordsGuard (computer science)Polygon (computer graphics)Boundary (topology)Simple polygonCombinatoricsCover (algebra)Regular polygonConvex hullMathematicsTime complexityComputer scienceGeometryMathematical analysisEngineering
DOInot available

Abstract

fetched live from OpenAlex

We study the problem of nding optimal covers of polygonal regions using multiple mobile guards. By our denition, a point is covered if, at some time, it lies within the convex hull of the guards from which it is visible. The denition captures our desire that guards both \see and \surround points that they cover. Guards move along continuous timeparameterized curves within a polygonal region P . An optimal m-guard cover of P is a set of m guard paths of minimum total length that cover all points in P . In this paper, we restrict our attention to the case where P is convex, and m is either two or three. We rst address the apparently simpler problem of optimally covering all points on the boundary, @P , of P . Although the guard paths are not restricted to @P , we prove that in every optimal two-guard boundary cover the guards remain on @P . When there are three guards, an optimal boundary cover may require a guard to cross the interior of the polygon. We show, however, that every optimal three-guard boundary cover is simple (i.e., guard paths do not cross one another). We provide complete characterizations of the form of optimal two- and three-guard boundary covers for convex polygons that support polynomial-time algorithms for their construction. Finally, we show that, for convex P , any optimal two- or three-guard cover of @P is also a (necessarily optimal) cover of the full polygon P .

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.000
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow)
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: none
GenreCandidate signal: Methods · Consensus signal: none
Teacher disagreement score0.868
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0010.001
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0010.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

Machine scores (provisional)

The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.041
GPT teacher head0.279
Teacher spread0.238 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it