Online Budgeted Repeated Matching

TL;DR

This paper studies an online resource allocation problem with multiple servers and capacity constraints, proposing algorithms with competitive guarantees for maximizing total job-server matching weights.

Contribution

It introduces competitive algorithms for online matching with capacity constraints, including a greedy approach and a load-balancing method for specific cases.

Findings

Greedy algorithm is 3-competitive when edge weights are at most half server capacity.

Randomized greedy algorithm is 6-competitive for unrestricted weights.

Load-balancing algorithm is near-optimal for small-weight jobs on parallel servers.

Abstract

A basic combinatorial online resource allocation problem is considered, where multiple servers have individual capacity constraints, and at each time slot, a set of jobs arrives, that have potentially different weights to different servers. At each time slot, a one-to-one matching has to be found between jobs and servers, subject to individual capacity constraints, in an online manner. The objective is to maximize the aggregate weight of jobs allotted to servers, summed across time slots and servers, subject to individual capacity constraints. This problem generalizes the well known adwords problem, and is also relevant for various other modern applications. A simple greedy algorithm is shown to be 3-competitive, whenever the weight of any edge is at most half of the corresponding server capacity. Moreover, a randomized version of the greedy algorithm is shown to be 6-competitive for the unrestricted edge weights case. For parallel servers with small-weight jobs, we show that a load-balancing algorithm is near-optimal.