Minimizing the Maximum Flow Time in the Online Food Delivery Problem

We study a common delivery problem encountered in nowadays online food-ordering platforms: Customers order dishes online, and the restaurant delivers the food after receiving the order. Specifically, we study a problem where k vehicles of capacity c are serving a set of requests ordering food from one restaurant. After a request arrives, it can be served by a vehicle moving from the restaurant to its delivery location. We are interested in serving all requests while minimizing the maximum flow-time, i.e., the maximum time length a customer waits to receive his/her food after submitting the order. We show that the problem is hard in both offline and online settings even when k = 1 and c = ?: There is a hardness of approximation of ?(n) for the offline problem, and a lower bound of ?(n) on the competitive ratio of any online algorithm, where n is number of points in the metric. We circumvent the strong negative results in two directions. Our main result is an O(1)-competitive online algorithm for the uncapacitated (i.e, c = ?) food delivery problem on tree metrics; we also have negative result showing that the condition c = ? is needed. Then we explore the speed-augmentation model where our online algorithm is allowed to use vehicles with faster speed. We show that a moderate speeding factor leads to a constant competitive ratio, and we prove a tight trade-off between the speeding factor and the competitive ratio

Minimizing Weighted lp-Norm of Flow-Time in the Rejection Model

We consider the online scheduling problem to minimize the weighted ell_p-norm of flow-time of jobs. We study this problem under the rejection model introduced by Choudhury et al. (SODA 2015) - here the online algorithm is allowed to not serve an eps-fraction of the requests. We consider the restricted assignments setting where each job can go to a specified subset of machines. Our main result is an immediate dispatch non-migratory 1/eps^{O(1)}-competitive algorithm for this problem when one is allowed to reject at most eps-fraction of the total weight of jobs arriving. This is in contrast with the speed augmentation model under which no online algorithm for this problem can achieve a competitive ratio independent of p

Speed-Oblivious Online Scheduling: Knowing (Precise) Speeds is not Necessary

We consider online scheduling on unrelated (heterogeneous) machines in a speed-oblivious setting, where an algorithm is unaware of the exact job-dependent processing speeds. We show strong impossibility results for clairvoyant and non-clairvoyant algorithms and overcome them in models inspired by practical settings: (i) we provide competitive learning-augmented algorithms, assuming that (possibly erroneous) predictions on the speeds are given, and (ii) we provide competitive algorithms for the speed-ordered model, where a single global order of machines according to their unknown job-dependent speeds is known. We prove strong theoretical guarantees and evaluate our findings on a representative heterogeneous multi-core processor. These seem to be the first empirical results for scheduling algorithms with predictions that are evaluated in a non-synthetic hardware environment.Comment: To appear at ICML 202

A Competitive Flow Time Algorithm for Heterogeneous Clusters Under Polytope Constraints

Modern data centers consist of a large number of heterogeneous resources such as CPU, memory, network bandwidth, etc. The resources are pooled into clusters for various reasons such as scalability, resource consolidation, and privacy. Clusters are often heterogeneous so that they can better serve jobs with different characteristics submitted from clients. Each job benefits differently depending on how much resource is allocated to the job, which in turn translates to how quickly the job gets completed. In this paper, we formulate this setting, which we term Multi-Cluster Polytope Scheduling (MCPS). In MCPS, a set of n jobs arrive over time to be executed on m clusters. Each cluster i is associated with a polytope P_i, which constrains how fast one can process jobs assigned to the cluster. For MCPS, we seek to optimize the popular objective of minimizing average weighted flow time of jobs in the online setting. We give a constant competitive algorithm with small constant resource augmentation for a large class of polytopes, which capture many interesting problems that arise in practice. Further, our algorithm is non-clairvoyant. Our algorithm and analysis combine and generalize techniques developed in the recent results for the classical unrelated machines scheduling and the polytope scheduling problem [10,12,11]