Pareto Optimal Matchings of Students to Courses in the Presence of Prerequisites

We consider the problem of allocating applicants to courses, where each applicant has a subset of acceptable courses that she ranks in strict order of preference. Each applicant and course has a capacity, indicating the maximum number of courses and applicants they can be assigned to, respectively. We thus essentially have a many-tomany bipartite matching problem with one-sided preferences, which has applications to the assignment of students to optional courses at a university. We consider additive preferences and lexicographic preferences as two means of extending preferences over individual courses to preferences over bundles of courses. We additionally focus on the case that courses have prerequisite constraints: we will mainly treat these constraints as compulsory, but we also allow alternative prerequisites. We further study the case where courses may be corequisites. For these extensions to the basic problem, we present the following algorithmic results, which are mainly concerned with the computation of Pareto optimal matchings (POMs). Firstly, we consider compulsory prerequisites. For additive preferences, we show that the problem of finding a POM is NP-hard. On the other hand, in the case of lexicographic preferences we give a polynomial-time algorithm for finding a POM, based on the well-known sequential mechanism. However we show that the problem of deciding whether a given matching is Pareto optimal is co-NP-complete. We further prove that finding a maximum cardinality (Pareto optimal) matching is NP-hard. Under alternative prerequisites, we show that finding a POM is NP-hard for either additive or lexicographic preferences. Finally we consider corequisites. We prove that, as in the case of compulsory prerequisites, finding a POM is NP-hard for additive preferences, though solvable in polynomial time for lexicographic preferences. In the latter case, the problem of finding a maximum cardinality POM is NP-hard and very difficult to approximate

A Compositional Framework for Preference-Aware Agents

A formal description of a Cyber-Physical system should include a rigorous specification of the computational and physical components involved, as well as their interaction. Such a description, thus, lends itself to a compositional model where every module in the model specifies the behavior of a (computational or physical) component or the interaction between different components. We propose a framework based on Soft Constraint Automata that facilitates the component-wise description of such systems and includes the tools necessary to compose subsystems in a meaningful way, to yield a description of the entire system. Most importantly, Soft Constraint Automata allow the description and composition of components' preferences as well as environmental constraints in a uniform fashion. We illustrate the utility of our framework using a detailed description of a patrolling robot, while highlighting methods of composition as well as possible techniques to employ them.Comment: In Proceedings V2CPS-16, arXiv:1612.0402

Priorities in the Location of Multiple Public Facilities

A collective decision problem is described by a set of agents, a profile of single-peaked preferences over the real line and a number k of public facilities to be located. We consider public facilities that do not suffer from congestion and are non-excludable. We provide a characterization of the class of rules satisfying Pareto-efficiency, object-population monotonicity and sovereignty. Each rule in the class is a priority rule that selects locations according to a predetermined priority ordering among "interest groups". We characterize each of the subclasses of priority rules that respectively satisfy anonymity, hiding-proofness and strategy-proofness. In particular, we prove that a priority rule is strategy-proof if and only if it partitions the set of agents into a fixed hierarchy. Alternatively, any such rule can be viewed as a collection of fixed-populations generalized peak-selection median rules (Moulin, 1980), that are linked across populations, in a way that we describe.Multiple public facilities; Priority rules; Hierarchical rules; Object-population monotonicity; Sovereignty; Anonymity; Strategy-proofness; Generalized median rules; Hiding-proofness

Truthful Assignment without Money

We study the design of truthful mechanisms that do not use payments for the generalized assignment problem (GAP) and its variants. An instance of the GAP consists of a bipartite graph with jobs on one side and machines on the other. Machines have capacities and edges have values and sizes; the goal is to construct a welfare maximizing feasible assignment. In our model of private valuations, motivated by impossibility results, the value and sizes on all job-machine pairs are public information; however, whether an edge exists or not in the bipartite graph is a job's private information. We study several variants of the GAP starting with matching. For the unweighted version, we give an optimal strategyproof mechanism; for maximum weight bipartite matching, however, we show give a 2-approximate strategyproof mechanism and show by a matching lowerbound that this is optimal. Next we study knapsack-like problems, which are APX-hard. For these problems, we develop a general LP-based technique that extends the ideas of Lavi and Swamy to reduce designing a truthful mechanism without money to designing such a mechanism for the fractional version of the problem, at a loss of a factor equal to the integrality gap in the approximation ratio. We use this technique to obtain strategyproof mechanisms with constant approximation ratios for these problems. We then design an O(log n)-approximate strategyproof mechanism for the GAP by reducing, with logarithmic loss in the approximation, to our solution for the value-invariant GAP. Our technique may be of independent interest for designing truthful mechanisms without money for other LP-based problems.Comment: Extended abstract appears in the 11th ACM Conference on Electronic Commerce (EC), 201

Dealing with inconsistent judgments in multiple criteria sorting models.

Sorting models consist in assigning alternatives evaluated on several criteria to ordered categories. To implement such models it is necessary to set the values of the preference parameters used in the model. Rather than fixing the values of these parameters directly, a usual approach is to infer these values from assignment examples provided by the decision maker (DM), i.e., alternatives for which (s)he specifies a required category. However, assignment examples provided by DMs can be inconsistent, i.e., may not match the sorting model. In such situations, it is necessary to support the DMs in the resolution of this inconsistency. In this paper, we extend algorithms from Mousseau et al.(2003) that calculate different ways to remove assignment examples so that the information can be represented in the sorting model. The extension concerns the possibility to relax (rather than to delete) assignment examples. These algorithms incorporate information about the confidence attached to each assignment example, hence providing inconsistency resolutions that the DMs are most likely to accept.Multicriteria decision aiding; Inconsistency analysis; Sorting problem;