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)

A key problem in combinatorial geometry is the identification of properties of a subset of a point set which has properties like convexity, monochromaticity, and emptiness. This thesis actual works on this sides of combinatorial geometry: efficiently finding empty monochromatic triangles in two-colored point sets on the plane. While earlier research focused on counting empty triangles in point set without any color, our work takes an optimal algorithm to explicitly detect them. By using geometric insights and visibility-based techniques. We then address a relaxed but equally compelling variant: monochromatic triangles containing at most one point of the opposite color. For this problem, we derive a quadratic lower bound, revealing how even slight relaxations in geometric constraints dramatically influence lower bound of empty monochromatic triangly in two colored point set.

Control Number

CS2302

DOI

https://dspace.isical.ac.in/items/c765b322-36d4-4ba5-b347-11b7e499911e

DSpace Identifier

http://hdl.handle.net/10263/7577

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