Online Multi-Commodity Flow with High Demands

TL;DR

This paper introduces a deterministic online algorithm for maximum benefit multi-commodity flow with high demands, capable of handling different request types and providing constant competitive ratio with capacity augmentation.

Contribution

It presents a novel online, bi-criteria algorithm for multi-commodity flow with high demands, handling diverse request types and extending to duration and scheduling scenarios.

Findings

Algorithm achieves constant competitive ratio.

Capacity augmentation is at most logarithmic.

Handles both low and high demand flow requests.

Abstract

This paper deals with the problem of computing, in an online fashion, a maximum benefit multi-commodity flow (\ONMCF), where the flow demands may be bigger than the edge capacities of the network. We present an online, deterministic, centralized, all-or-nothing, bi-criteria algorithm. The competitive ratio of the algorithm is constant, and the algorithm augments the capacities by at most a logarithmic factor. The algorithm can handle two types of flow requests: (i) low demand requests that must be routed along a path, and (ii) high demand requests that may be routed using a multi-path flow. Two extensions are discussed: requests with known durations and machine scheduling.