A Unified Approach to Online Matching with Conflict-Aware Constraints

Abstract

Online bipartite matching and allocation models are widely used to analyze and design markets such as Internet advertising, online labor, and crowdsourcing. Traditionally, vertices on one side of the market are fixed and known a priori, while vertices on the other side arrive online and are matched by a central agent to the offline side. The issue of possible conflicts among offline agents emerges in various real scenarios when we need to match each online agent with a set of offline agents.For example, in event-based social networks (e.g., Meetup), offline events conflict for some users since they will be unable to attend mutually-distant events at proximate times; in advertising markets, two competing firms may prefer not to be shown to one user simultaneously; and in online recommendation systems (e.g., Amazon Books), books of the same type “conflict” with each other in some sense due to the diversity requirement for each online buyer.The conflict nature inherent among certain offline agents raises significant challenges in both modeling and online algorithm design. In this paper, we propose a unifying model, generalizing the conflict models proposed in (She et al., TKDE 2016) and (Chen et al., TKDE 16). Our model can capture not only a broad class of conflict constraints on the offline side (which is even allowed to be sensitive to each online agent), but also allows a general arrival pattern for the online side (which is allowed to change over the online phase). We propose an efficient linear programming (LP) based online algorithm and prove theoretically that it has nearly-optimal online performance. Additionally, we propose two LP-based heuristics and test them against two natural baselines on both real and synthetic datasets. Our LP-based heuristics experimentally dominate the baseline algorithms, aligning with our theoretical predictions and supporting our unified approach.

Learning to Assign: Towards Fair Task Assignment in Large-Scale Ride Hailing

“…Task Assignment in Ride Hailing. Due to its fast expansion in metropolis, ride hailing has attracted extensive research interests [1,21,23,24,26], where a core topic is to assign taxi requests to drivers for certain optimization objects. Common goals in ride hailing include maximizing profit [23,26], minimizing travel cost [21,22], minimizing passengers' waiting time [1,24], and so on.…”

“…Many task assignment algorithms focus on providing theoretical performance guarantees [24]. However, they often make assumptions such as independence among drivers and assignments, which often prohibits them from delivering the expected performance in real-world applications.…”

“…The earnings ( ) = 0 if the driver is idle, whereas ( ) = / if he/she is serving request in batch . Unlike prior studies [21,24] that assume independent driver distributions across batches, we consider a more realistic dependency driver setting. That is, the driver distribution in future batches is influenced by that of the current batch as well as the current assignment.…”

“…Matching between taxi requests and drivers, a.k.a. task assignment, is the core issue in ride hailing research [19,21,23,24,26].…”

“…Existing studies mainly optimize task assignment from the perspective of the platform or the passengers, whereas few have investigated the problem from the drivers' perspective. For example, many assignment algorithms have been designed to maximize the utility [19,23,26] or minimize the travel cost [21] or the passengers' waiting time [24]. Only very recently did pioneer work [13,17] explore objectives such as balancing earnings among drivers during task assignment.…”