DISPATCH: An Optimal Algorithm for Online Perfect Bipartite Matching with i.i.d. Arrivals

by   Minjun Chang, et al.

This work presents the first algorithm for the problem of weighted online perfect bipartite matching with i.i.d. arrivals. Previous work only considered adversarial arrival sequences. In this problem, we are given a known set of workers, a distribution over job types, and non-negative utility weights for each worker, job type pair. At each time step, a job is drawn i.i.d. from the distribution over job types. Upon arrival, the job must be irrevocably assigned to a worker. The goal is to maximize the expected sum of utilities after all jobs are assigned. Our work is motivated by the application of ride-hailing, where jobs represent passengers and workers represent drivers. We introduce , a 0.5-competitive, randomized algorithm and prove that 0.5-competitive is the best possible. first selects a "preferred worker" and assign the job to this worker if it is available. The preferred worker is determined based on an optimal solution to a fractional transportation problem. If the preferred worker is not available, randomly selects a worker from the available workers. We show that maintains a uniform distribution over the workers even when the distribution over the job types is non-uniform.


page 1

page 2

page 3

page 4


DISPATCH: An Optimally-Competitive Algorithm for Maximum Online Perfect Bipartite Matching with i.i.d. Arrivals

This work presents the first algorithm for the problem of weighted onlin...

Scheduling Stochastic Real-Time Jobs in Unreliable Workers

We consider a distributed computing network consisting of a master and m...

Online Task Assignment Problems with Reusable Resources

We study online task assignment problem with reusable resources, motivat...

Improved Online Contention Resolution for Matchings and Applications to the Gig Economy

Motivated by applications in the gig economy, we study approximation alg...

Randomized algorithms for fully online multiprocessor scheduling with testing

We contribute the first randomized algorithm that is an integration of a...

Matching While Learning

We consider the problem faced by a service platform that needs to match ...

Subgame Perfect Equilibria of Sequential Matching Games

We study a decentralized matching market in which firms sequentially mak...

Please sign up or login with your details

Forgot password? Click here to reset