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Approximation Algorithms for Minimum Feedback Arc Set and Correlation Clustering

Ostovari Deylamani, Mojtaba | 2024

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 57807 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Zarei, Alireza
  7. Abstract:
  8. In this thesis, using linear programming, we present approximation algorithms for two groups of related problems, all of which are better than previously known algorithms in terms of approximation factor or running time. The first problem is the minimum feedback arc set on tournaments, a well-known NP-hard problem. In this problem, a tournament (complete directed weighted graph) is given as input, and the goal is to find a minimum-sized subset of its edges, whose removal makes the tournament acyclic. We will present a randomized 2.127-approximation algorithm based on the standard linear programming of this problem, for tournaments that satisfy probability constraints. We also introduce a combinatorial 3-approximation algorithm for this problem. For tournaments that satisfy both probability and triangle inequality constraints, we present an algorithm with an approximation factor of 5/3. The second problem is the weighted correlation clustering problem in which a set of vertices is given and for any pair of vertices, we have two weighted edges that indicate their difference and similarity. The aim is to find a clustering for the vertices that minimizes the sum of the difference weights of the pairs of vertices in the same cluster plus the sum of the similarity weights of the pairs of vertices in different clusters. For this problem, a randomized 3-approximation algorithm is presented if the input instance satisfies the probability constraints. We also introduce an algorithm with an approximation factor of 1.6 for the instances that satisfy both probability and triangle inequality constraints
  9. Keywords:
  10. Tournament ; Correlation Clustering ; Minimum Feedback Arc Set ; Rank Aggregation ; Approximate Algorithm

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