A Note on the Connection Between the Primal-Dual and the A* Algorithm

2010 ◽  
Vol 1 (1) ◽  
pp. 73-85 ◽  
Author(s):  
Xugang Ye ◽  
Shih-Ping Han ◽  
Anhua Lin
Keyword(s):  
Network Flow ◽  
Feasible Solution ◽  
Weighted Graph ◽  
Dual Algorithm ◽  
Heuristic Function ◽  
Network Flow Problems ◽  
A Algorithm ◽  
Flow Problems ◽  
Primal Dual ◽  
Initial Feasible Solution

The primal-dual algorithm for linear programming is very effective for solving network flow problems. For the method to work, an initial feasible solution to the dual is required. In this article, we show that, for the shortest path problem in a positively weighted graph equipped with a consistent heuristic function, the primal-dual algorithm will become the well-known A* algorithm if a special initial feasible solution to the dual is chosen. We also show how the improvements of the dual objective are related to the A* iterations.

A Note on the Connection Between the Primal-Dual and the A* Algorithm

2012 ◽  
pp. 170-181
Author(s):  
Xugang Ye ◽  
Shih-Ping Han ◽  
Anhua Lin
Keyword(s):  
Linear Programming ◽  
Network Flow ◽  
Feasible Solution ◽  
Weighted Graph ◽  
Shortest Path Problem ◽  
Dual Algorithm ◽  
A Algorithm ◽  
Flow Problems ◽  
Primal Dual ◽  
Initial Feasible Solution

The primal-dual algorithm for linear programming is very effective for solving network flow problems. For the method to work, an initial feasible solution to the dual is required. In this article, we show that, for the shortest path problem in a positively weighted graph equipped with a consistent heuristic function, the primal-dual algorithm will become the well-known A* algorithm if a special initial feasible solution to the dual is chosen. We also show how the improvements of the dual objective are related to the A* iterations.

A primal–dual simplex algorithm for bi-objective network flow problems

4OR ◽  
2008 ◽  
Vol 7 (3) ◽  
pp. 255-273 ◽  
Author(s):  
Augusto Eusébio ◽  
José Rui Figueira ◽  
Matthias Ehrgott
Keyword(s):  
Network Flow ◽  
Simplex Algorithm ◽  
Network Flow Problems ◽  
Flow Problems ◽  
Primal Dual ◽  
Dual Simplex ◽  
Dual Simplex Algorithm

scholarly journals Adaptation of Random Binomial Graphs for Testing Network Flow Problems Algorithms

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1716
Author(s):  
Adrian Marius Deaconu ◽  
Delia Spridon
Keyword(s):  
Network Flow ◽  
Large Scale ◽  
Random Network ◽  
Minimum Cost ◽  
Maximum Flow ◽  
Network Flow Problems ◽  
Commodity Flow ◽  
Vast Number ◽  
Flow Problems ◽  
Execution Speed

Algorithms for network flow problems, such as maximum flow, minimum cost flow, and multi-commodity flow problems, are continuously developed and improved, and so, random network generators become indispensable to simulate the functionality and to test the correctness and the execution speed of these algorithms. For this purpose, in this paper, the well-known Erdős–Rényi model is adapted to generate random flow (transportation) networks. The developed algorithm is fast and based on the natural property of the flow that can be decomposed into directed elementary s-t paths and cycles. So, the proposed algorithm can be used to quickly build a vast number of networks as well as large-scale networks especially designed for s-t flows.

Review of Network Flow Algorithms David P. Williamson

2021 ◽  
Vol 52 (1) ◽  
pp. 12-15
Author(s):  
S.V. Nagaraj
Keyword(s):  
Graduate Students ◽  
Real World ◽  
Network Flow ◽  
Network Flows ◽  
Optimization Problems ◽  
Capacity Constraints ◽  
Incoming Flow ◽  
Network Flow Problems ◽  
Flow Problems ◽  
Real World Problems

This book is on algorithms for network flows. Network flow problems are optimization problems where given a flow network, the aim is to construct a flow that respects the capacity constraints of the edges of the network, so that incoming flow equals the outgoing flow for all vertices of the network except designated vertices known as the source and the sink. Network flow algorithms solve many real-world problems. This book is intended to serve graduate students and as a reference. The book is also available in eBook (ISBN 9781316952894/US$ 32.00), and hardback (ISBN 9781107185890/US$99.99) formats. The book has a companion web site www.networkflowalgs.com where a pre-publication version of the book can be downloaded gratis.

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