No abstract

Matching with preferences has great potential to coordinate the efficient allocation of scarce resources in organizations when monetary transfers are not available. It is well known that it is impossible to combine all three properties of truthfulness, efficiency, and fairness (i.e., envy freeness) in matching with preferences. Established mechanisms are either efficient or envy free, and the efficiency loss in envy-free mechanisms is substantial. We focus on a widespread representative of a matching problem: course assignment where students have preferences for courses and organizers have priorities over students. An important feature in course assignment is that a course has a maximum capacity and a minimum required quota. This is also a requirement in many other matching applications, such as school choice, hospital-residents matching, or the assignment of workers to jobs. We introduce RESPCT, a mechanism that respects minimum quotas and is truthful, efficient, and has low levels of envy. The reduction in envy is significant and is due to two remarkably effective heuristics. We provide analytical and experimental results based on field data from a large-scale course assignment application. These results have led to a policy change and the proposed assignment system is now being used to match hundreds of students every semester.

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We study the problem of truthfully scheduling tasks to selfish unrelated machines, under the objective of makespan minimization, as was introduced in the seminal work of Nisan and Ronen [STOC'99]. Closing the current gap of [2.618, ] on the approximation ratio of deterministic truthful mechanisms is a notorious open problem in the field of algorithmic mechanism design. We provide the first such improvement in more than a decade, since the lower bounds of 2.414 (for = 3) and 2.618 (for → ∞) by Christodoulou et al. [SODA'07] and Koutsoupias and Vidali [MFCS'07], respectively. More specifically, we show that the currently best lower bound of 2.618 can be achieved even for just = 4 machines; for = 5 we already get the first improvement, namely 2.711; and allowing the number of machines to grow arbitrarily large we can get a lower bound of 2.755.