Minimum parametric flow over time

TL;DR

This paper introduces a novel labelling algorithm for solving dynamic minimum parametric network flow problems with linear lower bounds, efficiently computing flow values across parameter ranges.

Contribution

It develops a specialized labelling algorithm for parametric dynamic networks, enabling efficient computation of minimum flows over varying parameters.

Findings

Effective algorithm for parametric dynamic network flow

Computes flow values and breakpoints efficiently

Applicable to networks with linear lower bounds

Abstract

The paper presents a dynamic solution method for dynamic minimum parametric networks flow. The solution method solves the problem for a special parametric dynamic network with linear lower bound functions of a single parameter. Instead directly work on the original network, the method implements a labelling algorithm in the parametric dynamic residual network and uses quickest paths from the source node to the sink node in the time-space network along which repeatedly decreases the dynamic flow for a sequence of parameter values, in their increasing order. In each iteration, the algorithm computes both the minimum flow for a certain subinterval of the parameter values, and the new breakpoint for the maximum parametric dynamic flow value function.