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The School of Computer Science is pleased to present…

**Minimum Consistent Spanning Subset for Multi-Colored Trees **

**MSc Thesis Proposal by: Parham Khamsepour **

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**Date: Wednesday, December 7, 2022 **

**Time: 1:00 pm-2:00 pm **

**Location: Essex Hall, Room 122**** **

**Abstract:**** **

Given a set P of coloured points in the plane, the Minimum Consistent Subset (MCS) problem asks for a subset S of P such that every point of P is closest to a point with the same colour in S. This problem is widely used in areas involving nearest neighbours such as speech and handwriting recognition. This problem is NP-hard even for two-coloured point sets. The MCS problem can also be defined on graphs where the distance between two vertices is the length of the shortest path between them. We study a variant of the MCS problem on trees. This variant is called the Minimum Consistent Spanning Subset problem and has an extra constraint that the subset must span all the blocks in the tree, where a block is a maximal connected subtree of vertices of the same colour. We propose an algorithm that can correctly compute the Minimum Consistent Spanning Subset for a given multi-coloured tree using a bottom-up dynamic programming approach.

**Keywords: **Minimum Consistent Subset, Nearest neighbour, graph theory, dynamic programming

**MSc Thesis Committee: **** **

**Internal Reader:** Dr. Dan Wu

**External Reader: **Dr. Mehdi Sangani Monfared

**Advisor:** Dr. Ahmad Biniaz

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