A Fair Assignment Algorithm for Multiple Preference Queries

Consider an internship assignment system, where at the end of each academic year, interested university students search and apply for available positions, based on their preferences (e.g., nature of the job, salary, office location, etc). In a variety of facility, task or position assignment contexts, users have personal preferences expressed by different weights on the attributes of the searched objects. Although individual preference queries can be evaluated by selecting the object in the database with the highest aggregate score, in the case of multiple simultaneous requests, a single object cannot be assigned to more than one users. The challenge is to compute a fair 1-1 matching between the queries and the objects. We model this as a stable-marriage problem and propose an efficient method for its processing. Our algorithm iteratively finds stable query-object pairs and removes them from the problem. At its core lies a novel skyline maintenance technique, which we prove to be I/O optimal. We conduct an extensive experimental evaluation using real and synthetic data, which demonstrates that our approach outperforms adaptations of previous methods by several orders of magnitude

Profit Maximization with Sufficient Customer Satisfactions

In many commercial campaigns, we observe that there exists a tradeoff between the number of customers satisfied by the company and the profit gained. Merely satisfying as many customers as possible or maximizing the profit is not desirable. To this end, in this article, we propose a new problem called k - &lt;underline&gt;S&lt;/underline&gt;atisfiability &lt;underline&gt;A&lt;/underline&gt;ssignment for &lt;underline&gt;M&lt;/underline&gt;aximizing the &lt;underline&gt;P&lt;/underline&gt;rofit ( k -SAMP), where k is a user parameter and a non-negative integer. Given a set P of products and a set O of customers, k -SAMP is to find an assignment between P and O such that at least k customers are satisfied in the assignment and the profit incurred by this assignment is maximized. Although we find that this problem is closely related to two classic computer science problems, namely maximum weight matching and maximum matching, the techniques developed for these classic problems cannot be adapted to our k -SAMP problem. In this work, we design a novel algorithm called Adjust for the k -SAMP problem. Given an assignment A , Adjust iteratively increases the profit of A by adjusting some appropriate matches in A while keeping at least k customers satisfied in A . We prove that Adjust returns a global optimum. Extensive experiments were conducted that verified the efficiency of Adjust . </jats:p

Shortlisting Top-K Assignments

In this paper we identify a novel query type, the top-K assignment query (αTop-K). Consider a set of objects P and a set of suppliers S, where each object pi ∈ P must be assigned to one supplier sj ∈ S. Assume that there is a cost cij associated with every object-supplier pair 〈pi, sj〉. The matching with the smallest total cost would assign each object pi to the supplier sj with the minimum cij value. In many scenarios, however, runner-up assignments may be required too, like for example when a decision maker needs to make additional considerations, not captured by cij values. In this case, it is necessary to examine several shortlisted assignments before choosing one. This motivates the αTop-K query, which computes the K best assignments, i.e., those achieving the K smallest total costs. Algorithms for the traditional assignment ranking problem could be adapted to process the query, but their time requirements are prohibitive for large datasets (cubic to the input size). In this work we exploit the specific properties of the αTop-K problem and develop scalable methods for its processing. We also consider its incremental version, where K is not specified in advance; instead, the best assignments are iteratively computed on demand. An empirical evaluation with real data verifies the practicality and efficiency of our framework. 1