In multi-capacity ridesharing, multiple requests (e.g., customers, food items, parcels) with different origin and destination pairs travel in one resource. In recent years, online multi-capacity ridesharing services (i.e., where assignments are made online) like Uber-pool, foodpanda, and on-demand shuttles have become hugely popular in transportation, food delivery, logistics and other domains. This is because multi-capacity ridesharing services benefit all parties involved { the customers (due to lower costs), the drivers (due to higher revenues) and the matching platforms (due to higher revenues per vehicle/resource). Most importantly these services can also help reduce carbon emissions (due to fewer vehicles on roads). Online multi-capacity ridesharing is extremely challenging as the underlying matching graph is no longer bipartite (as in the unit-capacity case) but a tripartite graph with resources (e.g., taxis, cars), requests and request groups (combinations of requests that can travel together). The desired matching between resources and request groups is constrained by the edges between requests and request groups in this tripartite graph (i.e., a request can be part of at most one request group in the final assignment). While there have been myopic heuristic approaches employed for solving the online multi-capacity ridesharing problem, they do not provide any guarantees on the solution quality. To that end, this paper presents the first approach with bounds on the competitive ratio for online multi-capacity ridesharing (when resources rejoin the system at their initial location/depot after serving a group of requests).

中文翻译：

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在线多容量拼车的竞争比率

在多容量拼车中，具有不同来源和目的地对的多个请求（例如，客户、食品、包裹）在一种资源中传输。近年来，Uber-pool、foodpanda 和按需班车等在线多容量拼车服务（即在线分配）在交通、食品配送、物流等领域变得非常流行。这是因为多容量拼车服务使所有相关方受益{客户（由于成本较低）、司机（由于收入较高）和匹配平台（由于每辆车/资源的收入较高）。最重要的是，这些服务还有助于减少碳排放（由于道路上的车辆减少）。在线多容量拼车极具挑战性，因为底层匹配图不再是二分图（如在单位容量情况下），而是包含资源（例如，出租车、汽车）、请求和请求组（可以的请求的组合）的三方图。一起旅行）。资源和请求组之间所需的匹配受到此三方图中请求和请求组之间的边的约束（即，在最终分配中，请求最多可以是一个请求组的一部分）。虽然已经采用了短视的启发式方法来解决在线多容量拼车问题，但它们并没有对解决方案的质量提供任何保证。为此，