Date of Submission

2025

Date of Award

6-11-2025

Institute Name (Publisher)

Indian Statistical Institute

Document Type

Master's Dissertation

Degree Name

Master of Technology

Subject Name

Computer Science

Department

Advance Computing and Microelectronics Unit (ACMU-Kolkata)

Supervisor

Das, Sandip

Abstract (Summary of the Work)

The Planar-k-Centre problem is an important problem in the class of Optimal Facility Location problems, where given n points in the planar, the objective is finding the smallest k congruent discs such that their union encompasses all points. This dissertation examines a variant of this problem in which the L1 metric is used to determine the distances rather than the standard Euclidean metric, which we call L1P2C and a closely related problem which we call Undirected k Square Coverage where there is no directional constraint for the k squares which contain the given set of points. We have found two deterministic algorithms for the L1P2C problem, one operating in O(n log n) time and the other in O(n) time. Additionally, for k = 1, we have found an O(n log n) time method for the Undirected k Square Coverage problem.

Control Number

CS2322

DOI

https://dspace.isical.ac.in/items/c32e375e-7ec9-403c-a078-de4f6574faf6

DSpace Identifier

http://hdl.handle.net/10263/7561

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