English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We present a specialized network simplex algorithm for the budget-constrainedminimum cost flow problem, which is an extension of the traditional minimumcost flow problem by a second kind of costs associated with each edge, whosetotal value in a feasible flow is constrained by a given budget B. We present afully combinatorial description of the algorithm that is based on a novelincorporation of two kinds of integral node potentials and three kinds ofreduced costs. We prove optimality criteria and combine two methods that arecommonly used to avoid cycling in traditional network simplex algorithms intonew techniques that are applicable to our problem. With these techniques andour definition of the reduced costs, we are able to prove a pseudo-polynomialrunning time of the overall procedure, which can be further improved byincorporating Dantzig's pivoting rule. Moreover, we present computationalresults that compare our procedure with Gurobi.

A Network Simplex Method for the Budget-Constrained Minimum Cost Flow Problem