2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/132937We study the problem of assigning jobs to applicants. Each applicant has a weight and provides a preference list ranking a subset of the jobs. A matching M is popular if there is no other matching M' such that the weight of the applicants who prefer M' over M exceeds the weight of those who prefer M over M'. This paper gives efficient algorithms to find a popular matching if one exists.14 pages, 3 figures. A preliminary version appeared in the Proceedings of the 33rd International Colloquium on Automata, Languages and Programming (ICALP)Data Structures and AlgorithmsG.2.1text