Selecting a set of conflict-free group activities

• Main Authors: Lagman, Ghia Aniflauni, Lao, Angelyn R.
• Format: text
• Language: English
• Published: Animo Repository 2000
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/16998
• Institution: De La Salle University

This study introduced scheduling conflict-free group activities for a dating service with divorced couples as their clients. Here, conflict-free group activities refer to sequences of group activities where each client refuses to attend one common party or activity with his/her ex-spouse. This thesis would prove that it is possible to arrange a sequence of group activities in such a way that no two former couples attend the same party or activity, and yet each client parties exactly once with the other clients of the opposite sex. The problem is reformulated as a graph partitioning problem, which uses the concept of bipartite graph and biclique partition, and as matrix factorization problem, which uses the concept of reduced adjacency matrix. The researchers discussed the use of elementary linear algebra to solve the problem. Detailed proofs of some theorems and lemmas and illustrations of concepts through examples are given. This thesis is based mainly in Section 1 to 4 and the first 2 paragraphs of the Epilogue of the article entitled Scheduling Conflict-free Parties for a dating service by Bryan L. Shader and Chanyong Lee Shader.