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We consider the problem of allocating applicants to courses, where eachapplicant has a subset of acceptable courses that she ranks in strict order ofpreference. Each applicant and course has a capacity, indicating the maximumnumber of courses and applicants they can be assigned to, respectively. We thusessentially have a many-to-many bipartite matching problem with one-sidedpreferences, which has applications to the assignment of students to optionalcourses at a university. We consider additive preferences and lexicographicpreferences as two means of extending preferences over individual courses topreferences over bundles of courses. We additionally focus on the cases thatcourses have prerequisite constraints and where courses may be corequisites.  For these extensions to the basic problem, we present the followingalgorithmic results, which are mainly concerned with the computation of Paretooptimal matchings (POMs). Firstly, we consider compulsory prerequisites. Foradditive preferences, we show that the problem of finding a POM is NP-hard. Onthe other hand, in the case of lexicographic preferences we give apolynomial-time algorithm for finding a POM, based on the well-known sequentialmechanism. However we show that the problem of deciding whether a givenmatching is Pareto optimal is co-NP-complete. We further prove that finding amaximum cardinality (Pareto optimal) matching is NP-hard. Under alternativeprerequisites, we show that finding a POM is NP-hard for either additive orlexicographic preferences. Finally we consider corequisites. We prove that, asin the case of compulsory prerequisites, finding a POM is NP-hard for additivepreferences, though solvable in polynomial time for lexicographic preferences.In the latter case, the problem of finding a maximum cardinality POM is NP-hardand very difficult to approximate

Pareto optimal matchings of students to courses in the presence of prerequisites