Pith. sign in

REVIEW 4 major objections 4 minor 67 references

Efficient Mathematical Programming Formulation and Algorithmic Framework for Optimal Camera Placement

T0 review · 4 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Adaptive sampling plus integer programming can place cameras to cover 3.3–16.0% more space than random sampling at the same budget.

desk verdict A practical adaptive-sampling framework for camera placement with solid IP monotonicity, but the flood-fill visibility step is unvalidated and one TUS function is missing—worth refereeing with revisions. read the letter →

arxiv 2411.17942 v1 pith:HAIJPKBW submitted 2024-11-26 math.OC

Yash Kumar , Raghu Bollapragada , Benjamin D. Leibowicz This is my paper · ORCID
classification math.OC MSC 90C1090C2768U05
keywords cameraplacementmaximumk-coverageintegerprogrammingadaptivesamplingvisibilitycomputationflood-fillsurveillancesimulationoptimization
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper tries to establish that optimal camera placement in 3D environments can be made practical by iteratively generating candidate camera configurations with adaptive sampling and then solving a modified maximum k-coverage integer program to select the best network under a camera budget. The claimed payoff is that the Explore and Exploit strategy beats random sampling by 3.3–16.0% in coverage at equal budget, while Target Uncovered Spaces adds 6.9–9.1% in open, low-budget settings. Both adaptive strategies reportedly match the random-sampling baseline's coverage using only 30–70% of the sampling budget, which matters because visibility calculations dominate the computational cost. A sympathetic reader should care because the framework turns an NP-hard continuous problem into deployable placement decisions with measured gains over the standard random baseline.

What carries the argument

The load-bearing machinery is a feedback loop among three components. The optimizer is a modified maximum k-coverage integer program: each camera configuration is a set covering some free-space voxels, the program chooses at most k configurations subject to a cost budget and one-camera-per-neighborhood constraints, and the objective counts uniquely covered voxels. The visibility engine is a flood-fill algorithm that starts from voxels adjacent to the camera and expands to connected neighbors inside the field of view, only ray-casting for obstructions after the flood fill; this exploits the assumption that visible voxels form a single connected set. The sampling strategies generate new columns for the IP: E&E adds random exploratory configurations plus local perturbations of the previous optimal network, while TUS samples camera positions aimed at supervoxels with the largest uncovered-voxel counts.

What would settle it

Place a thin wall with a narrow doorway between two open volumes, discretize it at the paper's voxel resolution, and compare the flood-fill visible set with a brute-force ray cast from every voxel center; any missing voxel in the flood-fill output would show that the connected-component assumption fails and the reported coverage gains are not reliable for such scenes.

Watch

Extended reading notes

Core claim

The central claim is that a simulation-optimization loop can solve the camera placement problem in practice: sample candidate camera configurations, compute which free-space voxels each one sees, solve a maximum k-coverage integer program to pick the best subset, and use the previous solution to guide the next round of sampling. The Explore and Exploit strategy samples randomly for breadth and then adds configurations jittered around the current best network's positions and orientations; Target Uncovered Spaces samples supervoxels by how many uncovered voxels they contain and aims cameras at those blind spots. Across synthetic rooms of two sizes, two obstruction patterns, and two camera budgets, the authors report that E&E raises mean coverage by 3.3–16.0% over random sampling and TUS raises it by 6.9–9.1% in open, low-budget conditions, while both reach the random baseline's coverage with 30–70% of the sample budget. The paper also proves that coverage improves monotonically as samples are added, and demonstrates the method on a real apartment, where the optimized network tends to favor wall-face, near-ceiling placements over corner placements.

Load-bearing premise

The load-bearing premise is that the voxels visible from a camera form one connected component in the voxel grid at the chosen resolution, so the flood-fill visibility routine can reach every visible voxel by stepping through visible neighbors without ray-casting each one.

Editorial extensions

If this is right

  • Using E&E instead of one-shot random sampling raises final mean coverage by 3.3–16.0% across the tested room sizes, obstruction patterns, and camera budgets, with the largest gains in open, low-budget scenarios.
  • The adaptive strategies reach the random-sampling benchmark's coverage after spending only 30–70% of the sample budget, so equivalent coverage can be achieved with substantially fewer expensive visibility computations.
  • The greedy heuristic finds a marginally worse solution than the integer program in 14 of 40 instances and differs by about 1%, so it can stand in for the IP on very large problems or warm-start the IP for a provably optimal finish.
  • In real indoor layouts, the model's solutions place cameras along wall faces near ceilings rather than at corners, and with tight budgets they favor central positions that see into corridors and doorways.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • An extension the authors do not test: the same adaptive-sampling-plus-IP loop should transfer to other coverage-maximizing sensor problems, such as thermal cameras, LiDAR, or acoustic sensors, wherever coverage can be evaluated on a discrete grid.
  • Because coverage improves monotonically, warm-started re-optimization can track small environmental changes without losing the incumbent solution; this makes the framework usable for rapid redeployments, though the paper does not quantify that operational gain.
  • The 30–70% sample-budget saving suggests a practical scheduling benefit: stopping early gives a coverage guarantee relative to the random baseline, so a deployment team could trade final coverage for speed in time-critical situations.
  • The flood-fill visibility assumption is the main risk: in scenes with thin walls, narrow doorways, or clutter that breaks the connected chain of visible voxels, the coverage matrix fed to the IP would be wrong, and a ray-casting audit on such scenes would show how much the reported gains depend on that assumption.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. The paper proposes a simulation-optimization framework for camera placement: the environment is voxelized, candidate camera configurations are sampled by one of two adaptive strategies (Explore and Exploit, and Target Uncovered Spaces), visibility from each candidate is computed by a flood-fill algorithm, and a maximum-k-coverage integer program is solved iteratively over the growing candidate set. The authors prove monotonic improvements of the iterative scheme, give probability and expected-sample bounds for finding an optimal configuration by random sampling, and report coverage improvements of 3.3–16.0% over random sampling, with equivalent coverage at 30–70% of the sampling budget. A case study on the Replica apartment environment extracts practical placement insights. The mathematical programming formulation and the monotonicity argument are sound; the main unresolved issues are the unvalidated flood-fill visibility approximation, an undefined function in the TUS pseudocode, and the use of tuning environments that coincide with the final evaluation environments.

Significance. If the central claims are supported, the paper would be a useful practical contribution: it combines a clean integer-programming formulation with adaptive column-generation-style sampling, provides monotonicity and asymptotic-consistency guarantees, and demonstrates the approach on a realistic 3D indoor model. The theoretical bounds in Section 5 are correctly derived and are independent of the empirical results, which is a strength. However, the significance of the paper depends heavily on the credibility of the reported coverage numbers, and those numbers are currently computed with a visibility routine whose accuracy is neither proven nor compared against exact ray casting. The empirical claims also rest on a tuning setup that appears to reuse the benchmark environments. These issues must be resolved before the paper's main conclusions can be accepted.

major comments (4)
  1. [Section 4.3, Algorithm 2] The flood-fill visibility algorithm assumes that every visible free-space voxel is reachable from the camera by a 6-connected chain of free voxel centers that each pass the field-of-view test. The text states "As the visibility set is a connected set" to justify omitting large parts of the frustum, but this connectivity property is not proven and is not generally true: a visible region behind a narrow doorway, a thin column, or a diagonal slit can have a clear line of sight while no chain of face-adjacent voxel centers connects it to the camera. Since Vpd is the input to constraint (3) of IP (1)–(5) and drives all coverage statistics in Tables 2 and F1 and Figure 8, the headline coverage improvements and the 30–70% sampling-budget claim are computed from an unvalidated approximation. The appeal to "sufficient granularity" in Section 3.1 does not guarantee voxel-center connectivity. Please provide a correctness proof under explicit conditions, or replace the flood-fill with per-voxel ray casting, or at minimum validate the flood-fill against brute-force ray casting on the exact test environments and report the discrepancy.
  2. [Section 4.3, Algorithm 2] The TUS pseudocode calls the auxiliary function Linear-Visibility(p, vcenter, P), but this function is never defined anywhere in the manuscript or appendices. Footnote 2 only states that the computation is encoded in Linear-Visibility; no pseudocode, formula, or reference is given. Without this definition, the TUS algorithm is not implementable and all TUS results in Section 7, Figure 8, and Appendix F.3 depend on unspecified behavior. Please add a complete pseudocode block for Linear-Visibility and state its precise output semantics, including how it handles the case where no unobstructed camera position exists along the specified direction.
  3. [Section 7.1, Table 2] The hyperparameters for both adaptive strategies (fexploit, VPA, APA, iterations, func, supervoxel size, strict_vis_req) are selected in Appendix F.4 by evaluating on the same four environment types — medium/large, type 1/type 2 — that are later used for the final benchmark comparison in Table 2. This selection-on-test-data procedure means the reported 3.3–16.0% improvements over random sampling are not unbiased estimates of performance on new environments. Please either use a separate validation set for hyperparameter selection, or present a nested cross-validation/tuning protocol, or explicitly characterize the results as in-sample tuned performance. The current presentation overstates the generalizability of the empirical claims.
  4. [Section 7.1, Table 2] Each comparison in Table 2 uses only five trials per condition, and the reported ranges overlap even for headline cases: for Large 1 High, the RS range is [4583, 4814] and the E&E range is [4722, 4983], so the 3.33% mean improvement is not clearly separated from noise. No confidence intervals, paired tests, or adjustments for multiple comparisons are provided. For a stochastic simulation study, this is insufficient support for the abstract's quantitative claims of 3.3–16.0% improvement and 30–70% budget savings. Please report per-condition confidence intervals or paired significance tests, and discuss the overlap explicitly.
minor comments (4)
  1. [Section 5.2] The proof contains a typo: "P Dk+1 \ P Dk+1" should be "P Dk+1 \ P Dk". In addition, constraint (4) is restated with quantification over (p,d) in P Dk, whereas the original IP (1)–(5) quantifies over p in P; the notation should be aligned.
  2. [Appendix F.4.2] The caption and surrounding text for the angle perturbation allowance sensitivity analysis repeatedly refer to "voxel perturbation allowance" (VPA) when the quantity being varied is the angle perturbation allowance (APA). Please correct the captions and text to avoid confusing the two hyperparameters.
  3. [Appendix E] The derivation of |D| = O(1/epsilon^2) uses a volume-counting argument over representable floating-point values. Single-precision floating-point values are not uniformly distributed over the unit sphere, so the cardinality count is heuristic; if the lemma is only meant as an order-of-magnitude modeling bound, this should be stated explicitly.
  4. [Algorithm 1] The rejection loop for pnew ("while pnew = ∅ or pnew /∈ P") may be problematic when perturbations are continuous and P is a discrete voxel set; clarify how pnew is projected onto P and state the termination behavior of this loop.

Circularity Check

1 steps flagged · score 6.0 of 10

Headline coverage gains (3.3–16.0% and 30–70% sampling-budget savings) are measured on the same sanitized custom environments used to tune the adaptive strategies' hyperparameters, making the central empirical claims in-sample fits rather than independent predictions.

  1. fitted input called prediction [Section 7.1.1 (Table 2 and Figure 8) and Appendix F.4 (hyperparameter sensitivity analysis)]
    "The best hyperparameters, based on the results obtained in Appendix F.4, have then been used to test the strategies to compare final model performance. ... we run the two adaptive sampling model strategies under sanitized, custom environments and develop useful insights about them. ... tune the hyperparameters of each algorithm to use it for our final case study, where we implement the model on much larger, real-life scenarios."

    The hyperparameters of E&E and TUS (exploit fraction, voxel perturbation allowance, angle perturbation allowance, iteration count, uncovered search fraction, supervoxel size) are selected in Appendix F.4 by sensitivity analysis on the same sanitized room-generator environments (large and medium, type 1 and type 2) that Section 7 uses as the benchmark testbed. Table 2's reported 3.3–16.0% E&E improvements and Figure 8's claim that adaptive strategies match RS using only 30–70% of the sampling budget are therefore in-sample evaluations of settings tuned to maximize coverage on those exact environments. The RS baseline has no equivalent tuned hyperparameters, so the comparison is statistically forced and the headline numbers are not independent predictions.

full rationale

The derivation chain itself is largely self-contained: the paper does not rest its theoretical results on self-citations, and Propositions 2–4 (sampling probability, expected samples, and monotonic improvement) are standard arguments whose logic does not presuppose the empirical conclusions. No external uniqueness theorem or prior work by the same authors is invoked as load-bearing. The flood-fill visibility algorithm's assumption that the visible set is a single connected component is a genuine correctness risk (unproven for arbitrary meshes), but it is an input assumption rather than a circular reduction, so it does not by itself raise the circularity score. The one substantive circularity-adjacent problem is the tuning/evaluation overlap: Appendix F.4 tunes the adaptive strategies' hyperparameters on the same sanitized custom environments later used in Section 7 to quantify the headline coverage improvements and sampling-budget savings. Consequently the central empirical claims reduce to in-sample fits: the strategies are credited with gains on the very data used to set their knobs, while the random-sampling baseline receives no comparable tuning. The REPLICA case study in Section 6 is a separate, untuned application and retains independent evidentiary value, and the optimization framework's monotonicity property is independently valid. Because the framework has real independent content but its headline quantitative claims are contaminated by tuning-on-the-testbed, a partial circularity score of 6 is appropriate.

Assumptions & free parameters 7 free parameters · 7 assumptions · 1 invented entities

The framework rests on several unverified domain assumptions: the flood-fill visibility requires the visible voxel set to be connected, the voxel grid must be sufficiently fine, the roll angle is fixed to zero, the direction space is made finite by floating-point discretization, and the decimated mesh is assumed geometrically faithful. These are not proven but are standard simplifications.

free parameters (7)
  • fexploit (E&E exploration fraction) = 0.6
    Chosen via sensitivity analysis in Appendix F.4.2 on the same custom environments later used for final performance evaluation.
  • VPA (voxel perturbation allowance for E&E) = 1 voxel
    Chosen from {0,1,2,3,4} based on highest mean coverage and lowest range in Appendix F.4.2.
  • APA (angle perturbation allowance for E&E) = 30 degrees
    Chosen from {0,15,30,45} degrees in Appendix F.4.2; 30 degrees is marginally better for large rooms.
  • iterations (E&E and TUS) = 10
    Chosen over 5 and 20 iterations in Appendix F.4.2 due to tighter coverage ranges in large rooms.
  • func (TUS uncovered search fraction) = 0.4
    Chosen in Appendix F.4.3 as the value that performs better than RS in all tested cases.
  • supervoxel size (TUS) = 5
    Chosen in Appendix F.4.3 as a balance between mean coverage and range, though differences are small.
  • strict_vis_req (TUS) = False
    Appendix F.4.3 states that having a strict visibility requirement is detrimental; it is therefore deactivated.
assumptions (7)
  • domain assumption The visible set from a camera is a single connected component in the voxel grid.
    Used to justify the flood-fill visibility algorithm (Section 4.1, Algorithm 3) without formal proof or validation.
  • domain assumption Sufficient voxel granularity is maintained so that non-coverage of a voxel corresponds to almost or partial coverage by an obstacle.
    Explicitly assumed in Section 3.1; no convergence or error analysis is provided for the discretization.
  • domain assumption Camera roll angle is assumed to be zero.
    Stated in Section 3.1 as an easy extension, but treated as fixed throughout.
  • domain assumption The continuous direction space is discretized using single-precision floating-point representation.
    Needed to make the configuration space finite for the probability bounds in Section 5.
  • domain assumption Quadric decimation of the environment mesh preserves geometric fidelity for coverage calculations.
    The case study reduces the REPLICA mesh from 4.5M to 500K vertices (Section 6.1); no validation that coverage is unchanged is provided.
  • domain assumption The maximum k-coverage IP model is a valid representation of the optimal camera placement objective.
    The objective of maximizing covered voxels is treated as the natural problem objective in Section 3.2.
  • domain assumption The 'one camera per locale' constraint is well-defined by the immediate neighborhood set P Dadj_p.
    The notion of 'immediate neighborhood' is not precisely defined (Section 3.2.1), affecting the feasibility of solutions.
invented entities (1)
  • Supervoxel grid (TUS)
    purpose: An algorithmic construct to aggregate uncovered voxel counts and bias targeted sampling toward under-covered regions.
    A computational construct with no falsifiable handle outside the paper; its size is tuned in-sample.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Efficient Mathematical Programming Formulation and Algorithmic Framework for Optimal Camera Placement." pith.science (2026). https://pith.science/paper/HAIJPKBW

@misc{pith2026241117942,
  author       = {Pith},
  title        = {Pith review of: Efficient Mathematical Programming Formulation and Algorithmic Framework for Optimal Camera Placement},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HAIJPKBW}},
  note         = {Machine review of arXiv:2411.17942}
}
read the original abstract

Optimal camera placement plays a crucial role in applications such as surveillance, environmental monitoring, and infrastructure inspection. Even highly abstracted versions of this problem are NP-hard due to the high-dimensional continuous domain of camera configurations (i.e., positions and orientations) and difficulties in efficiently and accurately calculating camera coverage. In this paper, we present a novel framework for optimal camera placement that uses integer programming and adaptive sampling strategies to maximize coverage, given a limited camera budget. We develop a modified maximum k-coverage formulation and two adaptive sampling strategies, Explore and Exploit (E&E) and Target Uncovered Spaces (TUS), that iteratively add new camera configurations to the candidate set in order to improve the solution. E&E focuses on local search around camera configurations chosen in previous iterations, whereas TUS focuses specifically on covering regions that were previously uncovered. We first conduct theoretical analysis to provide bounds on the probability of finding an optimal solution and expected sampling needs, while ensuring monotonic improvements in coverage. Then, we conduct a detailed numerical analysis over different environments. Results show that E&E achieves coverage improvements of 3.3-16.0% over all baseline random sampling approaches, while maintaining manageable computational times. Meanwhile, TUS performs well in open environments and with tight camera budgets, achieving gains of 6.9-9.1% in such conditions. Compared to the baseline, our approach achieves similar coverage using only 30-70% of the sampling budget, demonstrating its computational efficiency. Through a case study, we obtain insights into optimal camera placement decisions for a typical indoor surveillance application.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

67 extracted references · 48 canonical work pages

  1. [1]

    , Adamaszek , A

    barticle Abrahamsen , M. , Adamaszek , A. , Miltzow , T. ( 2022 ) The Art Gallery Problem is R -complete . Journal of the ACM 69 ( 1 ), 1 -- 70 10.1145/3486220 barticle

    doi:10.1145/3486220 2022

  2. [2]

    , Delalic , S

    bchapter Alihodzic , A. , Delalic , S. , Hasic , D. ( 2020 ) An Exact Two - Phase Method For Optimal Camera Placement In Art Gallery Problem . 2020 15th Conference on Computer Science and Information Systems ( FedCSIS ) , pp. 215 -- 222 . 10.15439/2020F79 bchapter

    work page doi:10.15439/2020f79 2020

  3. [3]

    , Hassanein , H.S

    bchapter Ali , A. , Hassanein , H.S. ( 2021 ) Optimal Placement of Camera Wireless Sensors in Greenhouses . ICC 2021 - IEEE International Conference on Communications , pp. 1 -- 6 . 10.1109/ICC42927.2021.9500727 . ISSN: 1938-1883 bchapter

    arXiv 2021

  4. [4]

    ( 1998 ) Special Functions of Mathematics for Engineers

    bbook Andrews , L.C. ( 1998 ) Special Functions of Mathematics for Engineers . SPIE Press Monograph , vol. PM49 . SPIE Press , Bellingham, WA bbook

    work page 1998

  5. [5]

    , Ouafi , A

    barticle Aissaoui , A. , Ouafi , A. , Pudlo , P. , Gillet , C. , Baarir , Z.-E. , Taleb-Ahmed , A. ( 2018 ) Designing a camera placement assistance system for human motion capture based on a guided genetic algorithm . Virtual Reality 22 ( 1 ), 13 -- 23 10.1007/s10055-017-0310-7 barticle

    work page doi:10.1007/s10055-017-0310-7 2018

  6. [6]

    , Reithler , L

    bchapter Angella , F. , Reithler , L. , Gallesio , F. ( 2007 ) Optimal deployment of cameras for video surveillance systems . 2007 IEEE Conference on Advanced Video and Signal Based Surveillance , pp. 388 -- 392 . 10.1109/AVSS.2007.4425342 bchapter

    work page arXiv 2007

  7. [7]

    , Tirthapura , S

    bchapter Andersen , T. , Tirthapura , S. ( 2009 ) Wireless sensor deployment for 3D coverage with constraints . 2009 Sixth International Conference on Networked Sensing Systems ( INSS ) , pp. 1 -- 4 . 10.1109/INSS.2009.5409946 bchapter

    work page arXiv 2009

  8. [8]

    , Drenner , A

    barticle Bodor , R. , Drenner , A. , Schrater , P. , Papanikolopoulos , N. ( 2007 ) Optimal Camera Placement for Automated Surveillance Tasks . Journal of Intelligent and Robotic Systems 50 ( 3 ), 257 -- 295 10.1007/s10846-007-9164-7 barticle

    doi:10.1007/s10846-007-9164-7 2007

Show all 67 references
  1. [9]

    , Demir , A

    barticle Bai , Y. , Demir , A. , Yilmaz , A. , Sezen , H. ( 2024 ) Assessment and monitoring of bridges using various camera placements and structural analysis . Journal of Civil Structural Health Monitoring 14 ( 2 ), 321 -- 337 10.1007/s13349-023-00720-6 barticle

    2024 doi

  2. [10]

    , Johnson , E.L

    barticle Barnhart , C. , Johnson , E.L. , Nemhauser , G.L. , Savelsbergh , M.W.P. , Vance , P.H. ( 1998 ) Branch-and- Price : Column Generation for Solving Huge Integer Programs . Operations Research 46 ( 3 ), 316 -- 329 10.1287/opre.46.3.316 barticle

    1998 doi

  3. [11]

    , Jacobs , L.W

    barticle Brusco , M.J. , Jacobs , L.W. , Thompson , G.M. ( 1999 ) A morphing procedure to supplement a simulated annealing heuristic for cost‐ andcoverage‐correlated set‐covering problems . Annals of Operations Research 86 ( 0 ), 611 -- 627 10.1023/A:1018900128545 barticle

    1999 doi

  4. [12]

    ( 2009 ) Towards an Iterative Algorithm for the Optimal Boundary Coverage of a 3D Environment Bayro-Corrochano , E

    bchapter Bottino , A. ( 2009 ) Towards an Iterative Algorithm for the Optimal Boundary Coverage of a 3D Environment Bayro-Corrochano , E. , Eklundh , J.-O. (eds.) Progress in Pattern Recognition , Image Analysis , Computer Vision , And Applications , pp. 707 -- 715 . Springer ...

    2009 doi

  5. [13]

    , Padberg , M.W

    barticle Balas , E. , Padberg , M.W. ( 1972 ) On the Set - Covering Problem . Operations Research 20 ( 6 ), 1152 -- 1161 10.1287/opre.20.6.1152 barticle

    1972 doi

  6. [14]

    , Pereira , J

    barticle Bautista , J. , Pereira , J. ( 2007 ) A GRASP algorithm to solve the unicost set covering problem . Computers & Operations Research 34 ( 10 ), 3162 -- 3173 10.1016/j.cor.2005.11.026 barticle

    2007 doi

  7. [15]

    , Chaturvedi , D.K

    barticle Chaudhary , A.S. , Chaturvedi , D.K. ( 2017 ) Observing hotspots and power loss in solar photovoltaic array under shading effects using thermal imaging camera . Int. J. Electr. Mach. Drives 3 ( 1 ), 15 -- 23 barticle

    2017

  8. [16]

    , Cerulli , R

    barticle Carrabs , F. , Cerulli , R. , Mansini , R. , Moreschini , L. , Serra , D. ( 2024 ) Solving the Set Covering Problem with Conflicts on Sets : A new parallel GRASP . Computers & Operations Research 166 , 106620 10.1016/j.cor.2024.106620 barticle

    2024

  9. [17]

    , Davis , R.P

    barticle Chrissis , J.W. , Davis , R.P. , Miller , D.M. ( 1982 ) The dynamic set covering próblem . Applied Mathematical Modelling 6 ( 1 ), 2 -- 6 10.1016/S0307-904X(82)80015-2 barticle

    1982 doi

  10. [18]

    ( 1975 ) A combinatorial theorem in plane geometry

    barticle Chvátal , V. ( 1975 ) A combinatorial theorem in plane geometry . Journal of Combinatorial Theory, Series B 18 ( 1 ), 39 -- 41 10.1016/0095-8956(75)90061-1 barticle

    1975 doi

  11. [19]

    , Keller , J

    bchapter Cheng , P. , Keller , J. , Kumar , V. ( 2008 ) Time-optimal UAV trajectory planning for 3D urban structure coverage . 2008 IEEE / RSJ International Conference on Intelligent Robots and Systems , pp. 2750 -- 2757 . 10.1109/IROS.2008.4650988 . ISSN: 2153-0866 bchapter

    2008

  12. [20]

    , Rossi , A

    barticle Castaño , F. , Rossi , A. , Sevaux , M. , Velasco , N. ( 2014 ) A column generation approach to extend lifetime in wireless sensor networks with coverage and connectivity constraints . Computers & Operations Research 52 , 220 -- 230 10.1016/j.cor.2013.11.001 barticle

    2014 doi

  13. [21]

    , Toth , P

    barticle Caprara , A. , Toth , P. , Fischetti , M. ( 2000 ) Algorithms for the Set Covering Problem . Annals of Operations Research 98 ( 1 ), 353 -- 371 10.1023/A:1019225027893 barticle

    2000 doi

  14. [22]

    , Vasques , F

    barticle Costa , D.G. , Vasques , F. , Portugal , P. ( 2017 ) Enhancing the availability of wireless visual sensor networks: Selecting redundant nodes in networks with occlusion . Applied Mathematical Modelling 42 , 223 -- 243 10.1016/j.apm.2016.10.008 barticle

    2017 doi

  15. [23]

    , Hudry , O

    barticle Elloumi , S. , Hudry , O. , Marie , E. , Martin , A. , Plateau , A. , Rovedakis , S. ( 2021 ) Optimization of wireless sensor networks deployment with coverage and connectivity constraints . Annals of Operations Research 298 ( 1 ), 183 -- 206 10.1007/s10479-018-2943-7...

    2021 doi

  16. [24]

    , Sclaroff , S

    barticle Erdem , U.M. , Sclaroff , S. ( 2006 ) Automated camera layout to satisfy task-specific and floor plan-specific coverage requirements . Computer Vision and Image Understanding 103 ( 3 ), 156 -- 169 10.1016/j.cviu.2006.06.005 barticle

    2006 doi

  17. [25]

    , Moya , F.D

    barticle Fuentes , J.E. , Moya , F.D. , Montoya , O.D. ( 2020 ) Method for estimating solar energy potential based on photogrammetry from unmanned aerial vehicles . Electronics 9 ( 12 ), 2144 . Publisher: MDPI barticle

    2020

  18. [26]

    , Zhou , J

    barticle Fu , Y.-G. , Zhou , J. , Deng , L. ( 2014 ) Surveillance of a 2D Plane Area with 3D Deployed Cameras . Sensors 14 ( 2 ), 1988 -- 2011 10.3390/s140201988 barticle

    2014 doi

  19. [27]

    , Heckbert , P.S

    bchapter Garland , M. , Heckbert , P.S. ( 1997 ) Surface simplification using quadric error metrics . Proceedings of the 24th Annual Conference on Computer Graphics and Interactive Techniques . SIGGRAPH '97 , pp. 209 -- 216 . ACM Press/Addison-Wesley Publishing Co. , USA . 10....

    1997

  20. [28]

    ( 2010 ) Approximation Algorithms for Art Gallery Problems in Polygons and Terrains

    bchapter Ghosh , S.K. ( 2010 ) Approximation Algorithms for Art Gallery Problems in Polygons and Terrains . WALCOM : Algorithms and Computation vol. 5942 , pp. 21 -- 34 . Springer , Berlin, Heidelberg . 10.1007/978-3-642-11440-3_3 bchapter

    2010 doi

  21. [29]

    ( 1975 ) Polytopal graphs

    bchapter Grünbaum , B. ( 1975 ) Polytopal graphs . Studies in Graph Theory vol. 12 , pp. 201 -- 224 . The Mathematical Association of America , Washington bchapter

    1975

  22. [30]

    , Xiang , L

    barticle Gai , J. , Xiang , L. , Tang , L. ( 2021 ) Using a depth camera for crop row detection and mapping for under-canopy navigation of agricultural robotic vehicle . Computers and Electronics in Agriculture 188 , 106301 10.1016/j.compag.2021.106301 barticle

    2021

  23. [31]

    ( 1976 ) Mathematical Gems II

    bbook Honsberger , R. ( 1976 ) Mathematical Gems II . Published and distributed by the Mathematical Association of America , Washington . OCLC: 1257299219 bbook

    1976

  24. [32]

    , Pathria , A

    barticle Hochbaum , D.S. , Pathria , A. ( 1998 ) Analysis of the greedy approach in problems of maximum k-coverage . Naval Research Logistics (NRL) 45 ( 6 ), 615 -- 627 10.1002/(SICI)1520-6750(199809)45:6<615::AID-NAV5>3.0.CO;2-5 barticle

    1998 doi

  25. [33]

    , Chaudhury , S

    bchapter Indu , S. , Chaudhury , S. , Mittal , N.R. , Bhattacharyya , A. ( 2009 ) Optimal sensor placement for surveillance of large spaces . 2009 Third ACM / IEEE International Conference on Distributed Smart Cameras ( ICDSC ) , pp. 1 -- 8 . 10.1109/ICDSC.2009.5289398 bchapter

    2009

  26. [34]

    ( 2013 ) A Lagrangean -based heuristics for the target covering problem in wireless sensor network

    barticle Jarray , F. ( 2013 ) A Lagrangean -based heuristics for the target covering problem in wireless sensor network . Applied Mathematical Modelling 37 ( 10 ), 6780 -- 6785 10.1016/j.apm.2013.02.006 barticle

    2013 doi

  27. [35]

    , Brévilliers , M

    barticle Kritter , J. , Brévilliers , M. , Lepagnot , J. , Idoumghar , L. ( 2019 ) On the optimal placement of cameras for surveillance and the underlying set cover problem . Applied Soft Computing 74 , 133 -- 153 10.1016/j.asoc.2018.10.025 barticle

    2019 doi

  28. [36]

    2008 IEEE International Symposium on Circuits And Systems , pp

    bchapter Kenichi Yabuta , Hitoshi Kitazawa ( 2008 ) Optimum camera placement considering camera specification for security monitoring . 2008 IEEE International Symposium on Circuits And Systems , pp. 2114 -- 2117 . IEEE , Seattle, WA, USA . 10.1109/ISCAS.2008.4541867 bchapter

    2008

  29. [37]

    , Ham , Y

    barticle Kim , J. , Ham , Y. , Chung , Y. , Chi , S. ( 2019 ) Systematic Camera Placement Framework for Operation - Level Visual Monitoring on Construction Jobsites . Journal of Construction Engineering and Management 145 ( 4 ), 04019019 10.1061/(ASCE)CO.1943-7862.0001636 barticle

    2019

  30. [38]

    , Lattanzi , D

    bchapter Khaloo , A. , Lattanzi , D. ( 2015 ) A Hierarchical Computer Vision Approach to Infrastructure Inspection . Computing in Civil Engineering 2015 , pp. 540 -- 547 . American Society of Civil Engineers , Austin, Texas . 10.1061/9780784479247.067 bchapter

    2015 doi

  31. [39]

    , Moss , A

    barticle Khuller , S. , Moss , A. , Naor , J.S. ( 1999 ) The budgeted maximum coverage problem . Information Processing Letters 70 ( 1 ), 39 -- 45 10.1016/S0020-0190(99)00031-9 barticle

    1999 doi

  32. [40]

    , Pocchiola , M

    botherref Kranakis , E. , Pocchiola , M. A Brief Survey of Art Gallery Problems in Integer Lattice Systems botherref

  33. [41]

    (1981) Area flooding algorithms

    botherref Levoy , M. (1981) Area flooding algorithms. Two-Dimensional Computer Animation, Course Notes 9 for SIGGRAPH 82 botherref

    1981

  34. [42]

    , Mei , Y

    barticle Liu , K. , Mei , Y. , Shi , J. ( 2015 ) An Adaptive Sampling Strategy for Online High - Dimensional Process Monitoring . Technometrics 57 ( 3 ), 305 -- 319 10.1080/00401706.2014.947005 barticle

    2015

  35. [43]

    , Rainforth , T

    barticle Lu , X. , Rainforth , T. , Teh , Y.W. ( 2023 ) Daisee: Adaptive importance sampling by balancing exploration and exploitation . Scandinavian Journal of Statistics 50 ( 3 ), 1298 -- 1324 10.1111/sjos.12637 barticle

    2023 doi

  36. [44]

    , Aouf , N

    barticle Morsly , Y. , Aouf , N. , Djouadi , M.S. , Richardson , M. ( 2012 ) Particle Swarm Optimization Inspired Probability Algorithm for Optimal Camera Network Placement . IEEE Sensors Journal 12 ( 5 ), 1402 -- 1412 10.1109/JSEN.2011.2170833 . Conference Name: IEEE Sensors ...

    2012

  37. [45]

    The three-dimensional art gallery problem and its solutions

    botherref Marzal , J. The three-dimensional art gallery problem and its solutions. PhD Thesis , Murdoch University (2012). https://researchportal.murdoch.edu.au/esploro/outputs/doctoral/The-three-dimensional-art-gallery-problem-and/991005541831107891 botherref

    2012

  38. [46]

    , Kim , K

    barticle Murray , A.T. , Kim , K. , Davis , J.W. , Machiraju , R. , Parent , R. ( 2007 ) Coverage optimization to support security monitoring . Computers, Environment and Urban Systems 31 ( 2 ), 133 -- 147 10.1016/j.compenvurbsys.2006.06.002 barticle

    2007 doi

  39. [47]

    , Parasuraman , R

    botherref Munir , A. , Parasuraman , R. Analysis of Exploration vs. Exploitation in Adaptive Information Sampling . arXiv. arXiv:2111.11384 (2021). 10.48550/arXiv.2111.11384 botherref

    2021 doi arXiv

  40. [48]

    , Trumbore , B

    barticle Möller , T. , Trumbore , B. ( 1997 ) Fast, Minimum Storage Ray - Triangle Intersection . Journal of Graphics Tools 2 ( 1 ), 21 -- 28 10.1080/10867651.1997.10487468 barticle

    1997

  41. [49]

    , Baybars , I

    barticle Nishizeki , T. , Baybars , I. ( 1979 ) Lower bounds on the cardinality of the maximum matchings of planar graphs . Discrete Mathematics 28 ( 3 ), 255 -- 267 10.1016/0012-365X(79)90133-X barticle

    1979 doi

  42. [50]

    , Mei , Y

    barticle Nabhan , M. , Mei , Y. , Shi , J. ( 2021 ) Correlation-based dynamic sampling for online high dimensional process monitoring . Journal of Quality Technology 53 ( 3 ), 289 -- 308 10.1080/00224065.2020.1726717 barticle

    2021

  43. [51]

    ( 1987 ) Art Gallery Theorems and Algorithms

    bbook O'Rourke , J. ( 1987 ) Art Gallery Theorems and Algorithms . The international series of monographs on computer science , vol. 3 . Oxford Univ. Press , New York, NY bbook

    1987

  44. [52]

    , Fantini , C

    bchapter Penha , E. , Fantini , C. , Chaimowicz , L. ( 2013 ) Coverage in Arbitrary 3D Environments The Art Gallery Problem in Shooter Games . https://api.semanticscholar.org/CorpusID:56033743 bchapter

    2013

  45. [53]

    , Le Berre , M

    barticle Rebai , M. , Le Berre , M. , Hnaien , F. , Snoussi , H. ( 2016 ) Exact Biobjective Optimization Methods for Camera Coverage Problem in Three - Dimensional Areas . IEEE Sensors Journal 16 ( 9 ), 3323 -- 3331 10.1109/JSEN.2016.2519451 barticle

    2016

  46. [54]

    , Le berre , M

    barticle Rebai , M. , Le berre , M. , Snoussi , H. , Hnaien , F. , Khoukhi , L. ( 2015 ) Sensor deployment optimization methods to achieve both coverage and connectivity in wireless sensor networks . Computers & Operations Research 59 , 11 -- 21 10.1016/j.cor.2014.11.002 barticle

    2015 doi

  47. [55]

    , Huang , Q

    bchapter Sun , Y. , Huang , Q. , Hsiao , D.-Y. , Guan , L. , Hua , G. ( 2021 ) Learning View Selection for 3D Scenes , pp. 14464 -- 14473 . https://openaccess.thecvf.com/content/CVPR2021/html/Sun_Learning_View_Selection_for_3D_Scenes_CVPR_2021_paper.html bchapter

    2021

  48. [56]

    , Moehrle , N

    barticle Smith , N. , Moehrle , N. , Goesele , M. , Heidrich , W. ( 2018 ) Aerial path planning for urban scene reconstruction: a continuous optimization method and benchmark . ACM Transactions on Graphics 37 ( 6 ), 1 -- 15 10.1145/3272127.3275010 barticle

    2018

  49. [57]

    , Parada , V

    barticle Solar , M. , Parada , V. , Urrutia , R. ( 2002 ) A parallel genetic algorithm to solve the set-covering problem . Computers & Operations Research 29 ( 9 ), 1221 -- 1235 10.1016/S0305-0548(01)00026-0 barticle

    2002 doi

  50. [58]

    , Whelan , T

    botherref Straub , J. , Whelan , T. , Ma , L. , Chen , Y. , Wijmans , E. , Green , S. , Engel , J.J. , Mur-Artal , R. , Ren , C. , Verma , S. , Clarkson , A. , Yan , M. , Budge , B. , Yan , Y. , Pan , X. , Yon , J. , Zou , Y. , Leon , K. , Carter , N. , Briales , J. , Gillingh...

    2019 arXiv

  51. [59]

    , Le Josse , N

    barticle Thuillier , O. , Le Josse , N. , Olteanu , A.-L. , Sevaux , M. , Tanguy , H. ( 2024 ) Efficient configuration of heterogeneous multistatic sonar networks: A mixed-integer linear programming approach . Computers & Operations Research 167 , 106637 10.1016/j.cor.2024.106...

    2024

  52. [60]

    ( 2001 ) A Technical Review of Column Generation in Integer Programming

    barticle Wilhelm , W.E. ( 2001 ) A Technical Review of Column Generation in Integer Programming . Optimization and Engineering 2 ( 2 ), 159 -- 200 10.1023/A:1013141227104 . Accessed 2024-11-19 barticle

    2001 doi

  53. [61]

    , Zhang , H

    barticle Wang , X. , Zhang , H. , Gu , H. ( 2020 ) Solving Optimal Camera Placement Problems in IoT Using LH - RPSO . IEEE Access 8 , 40881 -- 40891 10.1109/ACCESS.2019.2941069 barticle

    2020

  54. [62]

    , Li , H

    barticle Yang , X. , Li , H. , Huang , T. , Zhai , X. , Wang , F. , Wang , C. ( 2018 ) Computer‐ Aided Optimization of Surveillance Cameras Placement on Construction Sites . Computer-Aided Civil and Infrastructure Engineering 33 ( 12 ), 1110 -- 1126 10.1111/mice.12385 barticle

    2018 doi

  55. [63]

    , Yarmani , M.E

    barticle Yaagoubi , R. , Yarmani , M.E. , Kamel , A. , Khemiri , W. ( 2015 ) HybVOR : A Voronoi - Based 3D GIS Approach for Camera Surveillance Network Placement . ISPRS International Journal of Geo-Information 4 ( 2 ), 754 -- 782 10.3390/ijgi4020754 barticle

    2015 doi

  56. [64]

    , Ewald , D

    barticle Zarzycki , H. , Ewald , D. , Prokopowicz , P. ( 2024 ) Leveraging Swarm Intelligence for Optimal Thermal Camera and Sensor Placement in Industrial Environments . Electronics 13 ( 3 ), 601 10.3390/electronics13030601 barticle

    2024 doi

  57. [65]

    , Wang , D

    barticle Zan , X. , Wang , D. , Xian , X. ( 2023 ) Spatial Rank - Based Augmentation for Nonparametric Online Monitoring and Adaptive Sampling of Big Data Streams . Technometrics 65 ( 2 ), 243 -- 256 10.1080/00401706.2022.2143903 barticle

    2023

  58. [66]

    , Xia , L

    bchapter Zhang , H. , Xia , L. , Tian , F. , Wang , P. , Cui , J. , Tang , C. , Deng , N. , Ma , N. ( 2013 ) An optimized placement algorithm for collaborative information processing at a wireless camera network . 2013 IEEE International Conference on Multimedia and Expo ( ICM...

    2013

  59. [67]

    write newline

    " write newline "" before.all 'output.state := FUNCTION string.to.integer 't := t text.length 'k := #1 'char.num := t char.num #1 substring 's := s is.num s "." = or char.num k = not and char.num #1 + 'char.num := while char.num #1 - 'char.num := t #1 char.num substring FUNCTI...

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.