Call for Paper - January 2023 Edition
IJCA solicits original research papers for the January 2023 Edition. Last date of manuscript submission is December 20, 2022. Read More

Development of Algorithm for Identification of Area for Maximum Coverage and Interference

Print
PDF
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Year of Publication: 2017
Authors:
Janak Gupta, Pankaj Kumar
10.5120/ijca2017915323

Janak Gupta and Pankaj Kumar. Development of Algorithm for Identification of Area for Maximum Coverage and Interference. International Journal of Computer Applications 173(6):10-13, September 2017. BibTeX

@article{10.5120/ijca2017915323,
	author = {Janak Gupta and Pankaj Kumar},
	title = {Development of Algorithm for Identification of Area for Maximum Coverage and Interference},
	journal = {International Journal of Computer Applications},
	issue_date = {September 2017},
	volume = {173},
	number = {6},
	month = {Sep},
	year = {2017},
	issn = {0975-8887},
	pages = {10-13},
	numpages = {4},
	url = {http://www.ijcaonline.org/archives/volume173/number6/28338-2017915323},
	doi = {10.5120/ijca2017915323},
	publisher = {Foundation of Computer Science (FCS), NY, USA},
	address = {New York, USA}
}

Abstract

In this paper we consider the following problem: Given a set n shops of Store1 in the plane P than how many minimum shops of Store2 to be open for the maximum coverage and interference Store1 Shops. The problem is solve using the Stabbing disk induced by points on the plane P. For a point set P, where no two points have the same x or y coordinates, derive an upper bound on the size of the stabbing set of n/2 axis-parallel rectangles induced by each pair of points a,b ∈ P as the diagonal of the rectangles. For a point set P in convex position, derive a lower bound on the size of the stabbing set n/2 axis-parallel rectangles induced by each pair of points a,b∈P as the diagonal of the rectangles.

References

  1. Boris Aronow, Muriel Dulieu, and ferran Hurtado, “Witness Gabriel graphs”, 2010.
  2. Boris aronov, Muriel dulieu, and ferranhurtado, “Witness Delaunay graphs”, Computational geometry: theory and application 44:329:344,2011.
  3. M.D. Berg, O.Cheong, M. Kreveld, and M. Overmars, “Computational geometry”, Algorithms and Application Springer 3rd edition, 2008.
  4. G. Di Battista, p. edes, R. tamassia, and I.G. Tollis., “Graph drawing. Algorithms For the visualization of graphs”, Prentice hall, 1999.
  5. Robert J. Fowler, Mike Paterson and steven L. Tanimoto, “Optimal packing and covering in the plane are np- complete”,Inf process. Lett.,12(3):133-137, 1981.
  6. K. R. Gabriel and R.r.sokal, “A new statistical approach to geographic variation analysis”, Systematic Zoology, 18:259-278, 1969.
  7. J. W. Jaromczyk and G.T. Toussaint, “Relative neighbourhood graphs and their relatives”, Proc. IEEE, 80:1502-1517,1992.
  8. G. Liotta, “Proximity drawings”, In inrr. Tamassia, editor, handbook of graphs drawing and visualization . CRC press.
  9. Frank Nielsen,“Fast stabbing of boxes in high dimension”, Theoretical computer science, 246(1/2):53-75, 2000.
  10. G. T. Toussaint, “Geometric proximity graphs for improving nearest neighbor methods in instance based learning and data mining”, International Journal of Computer Geom. And Applications. 15(2).
  11. G. T. Toussaint, “Some unsolved problems on proximity graphs”, 1991

Keywords

Stabbing, Proximity Graph, Gabriel Graphs, Triangulation, Neighborliness, Convex hull,rectangle stabbing.