On Conflict-Free Chromatic Guarding of Simple Polygons

Çağırıcı, Onur; Ghosh, Subir; Hliněný, Petr; Roy, Bishnupada

doi:10.1007/978-3-030-36412-0_49

Cited by 7 publications

(5 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Those four guards see vertices p 1 and Fig. 3 (a) A bowl-shaped gadget [2]. (b) A guard on p 1 or p 2 can see all the vertices of {a 1 , a 2 , .…”

Section: Bowl-shaped Gadgets and Pocket Gadgetsmentioning

confidence: 99%

“…The chromatic art gallery problem was motivated by the following application [2], [7]. Consider the problem of navigating a robot inside a polygon, where the robot communicates with radio beacons.…”

Section: Introductionmentioning

confidence: 99%

“…Copyright c 2023 The Institute of Electronics, Information and Communication Engineers free chromatic guarding problem [2]; they proved the NPhardness of the problem when the number of colors is k = 2. However, they mentioned that their proof does not imply the NP-hardness for the vertex-to-point case.…”

Section: Introductionmentioning

confidence: 99%

“…Fig.4(a) The green area surrounded by a 10-vertex chain from a 1 to a 2 is called a pocket-gadget[2]. (b) A pair of red and blue guards on door vertices of bowls can see the inside of the pocket in the conflict-free condition.…”

mentioning

confidence: 99%

See 3 more Smart Citations

Computational Complexity of the Vertex-to-Point Conflict-Free Chromatic Art Gallery Problem

IWAMOTO,

IBUSUKI

2023

IEICE Trans. Inf. & Syst.

View full text Add to dashboard Cite

The art gallery problem is to find a set of guards who together can observe every point of the interior of a polygon P. We study a chromatic variant of the problem, where each guard is assigned one of k distinct colors. A chromatic guarding is said to be conflict-free if at least one of the colors seen by every point in P is unique (i.e., each point in P is seen by some guard whose color appears exactly once among the guards visible to that point). In this paper, we consider vertex-to-point guarding, where the guards are placed on vertices of P, and they observe every point of the interior of P. The vertex-to-point conflict-free chromatic art gallery problem is to find a colored-guard set such that (i) guards are placed on P's vertices, and (ii) any point in P can see a guard of a unique color among all the visible guards. In this paper, it is shown that determining whether there exists a conflict-free chromatic vertex-guard set for a polygon with holes is NP-hard when the number of colors is k = 2.

show abstract

“…Those four guards see vertices p 1 and Fig. 3 (a) A bowl-shaped gadget [2]. (b) A guard on p 1 or p 2 can see all the vertices of {a 1 , a 2 , .…”

Section: Bowl-shaped Gadgets and Pocket Gadgetsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Computational Complexity of the Vertex-to-Point Conflict-Free Chromatic Art Gallery Problem

IWAMOTO,

IBUSUKI

2023

IEICE Trans. Inf. & Syst.

View full text Add to dashboard Cite

show abstract

“…The sketch presents some key intuitions behind the full proof. It is based on the "window partition" by Suri [34], which was used in a similar fashion to approximate chromatic variants of the well-known art gallery problem [8,10].…”

Section: Proposition 42 There Is a Polynomial-time Algorithm That Tak...mentioning

confidence: 99%

Colouring polygon visibility graphs and their generalizations

Davies¹,

Krawczyk²,

McCarty³

et al. 2021

Preprint

View full text Add to dashboard Cite

Curve pseudo-visibility graphs generalize polygon and pseudo-polygon visibility graphs and form a hereditary class of graphs. We prove that every curve pseudo-visibility graph with clique number ω has chromatic number at most 3 • 4 ω−1 . The proof is carried through in the setting of ordered graphs; we identify two conditions satisfied by every curve pseudo-visibility graph (considered as an ordered graph) and prove that they are sufficient for the claimed bound. The proof is algorithmic: both the clique number and a colouring with the claimed number of colours can be computed in polynomial time.

show abstract