scholarly journals Approximate Algorithms for Continuous-Time Quickest Multi-Commodity Contraflow Problem

2020 ◽  
Vol 37 (1-2) ◽  
pp. 30-46
Author(s):  
Shiva Prakash Gupta ◽  
Durga Prasad Khanal ◽  
Urmila Pyakurel ◽  
Tanka Nath Dhamala
Keyword(s):  
Approximation Algorithms ◽  
Polynomial Time ◽  
Continuous Time ◽  
Flow Problem ◽  
Capacity Constraints ◽  
Approximate Algorithms ◽  
Optimal Solutions ◽  
Commodity Flow ◽  
Flow Problems

Multi-commodity flow problem appears when several distinct commodities are shipped from supply nodes to the demand nodes through a network without violating the capacity constraints. The quickest multi-commodity flow problem deals with the minimization of time satisfying given demand. Ingeneral, the quickest multi-commodity flow problems are computationally hard. The outbound lane capacities can be increased through reverting the orientation of lanes towards the demand nodes. We present two approximation algorithms by introducing partial contraow technique in the continuous-time quick estmulti-commodity ow problem: one polynomial-time with the help of length-bounded flow and another FPTAS by using _-condensed time-expanded graph. Both algorithms reverse only necessary arc capacities to get the optimal solutions and save unused arc capacities which may be used for other purposes.   

scholarly journals Maximum Multicommodity Flow with Intermediate Storage

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Durga Prasad Khanal ◽  
Urmila Pyakurel ◽  
Tanka Nath Dhamala
Keyword(s):  
Continuous Time ◽  
Flow Problem ◽  
Natural Transformation ◽  
Capacity Constraints ◽  
Multicommodity Flow ◽  
Flow Problems ◽  
Transit Times ◽  
Multicommodity Flow Problem ◽  
Intermediate Storage

The multicommodity flow problem deals with the transshipment of more than one commodity from respective sources to corresponding sinks without violating the capacity constraints. Due to the capacity constraints, flows out from the sources may not reach their sinks, and so, the storage of excess flows at intermediate nodes plays an important role in the maximization of flow values. In this paper, we introduce the maximum static as well as maximum dynamic multicommodity flow problems with intermediate storage. We present polynomial and pseudopolynomial time algorithms for the former and latter problems, respectively. We also present the solution procedures to these problems in contraflow network having symmetric as well as asymmetric arc transit times. We transform the solutions in continuous-time settings by using natural transformation.

BINDING ALGORITHM FOR POWER OPTIMIZATION BASED ON NETWORK FLOW METHOD

2002 ◽  
Vol 11 (03) ◽  
pp. 259-271 ◽  
Author(s):  
YOONSEO CHOI ◽  
TAEWHAN KIM
Keyword(s):  
Network Flow ◽  
Power Optimization ◽  
Flow Problem ◽  
Minimum Cost ◽  
Maximum Flow ◽  
Data Flow Graph ◽  
Commodity Flow ◽  
Behavioral Synthesis ◽  
Flow Problems ◽  
Step Procedure

We propose an efficient binding algorithm for power optimization in behavioral synthesis. In prior work, it has been shown that several binding problems for low-power can be formulated as multi-commodity flow problems (due to an iterative execution of data flow graph) and be solved optimally. However, since the multi-commodity flow problem is NP-hard, the application is limited to a class of small sized problems. To overcome the limitation, we address the problem of how we can effectively make use of the property of efficient flow computations in a network so that it is extensively applicable to practical designs while producing close-to-optimal results. To this end, we propose a two-step procedure, which (1) determines a feasible binding solution by partially utilizing the computation steps for finding a maximum flow of minimum cost in a network and then (2) refines it iteratively. Experiments with a set of benchmark examples show that the proposed algorithm saves the run time significantly while maintaining close-to-optimal bindings in most practical designs.

scholarly journals Efficient Algorithms on Multicommodity Flow over Time Problems with Partial Lane Reversals

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Urmila Pyakurel ◽  
Shiva Prakash Gupta ◽  
Durga Prasad Khanal ◽  
Tanka Nath Dhamala
Keyword(s):  
Polynomial Time ◽  
Flow Problem ◽  
Maximum Flow ◽  
Multicommodity Flow ◽  
Time Step ◽  
Approximation Solution ◽  
Flow Problems ◽  
Time Problem ◽  
Flow Over Time ◽  
Over Time

The multicommodity flow problem arises when several different commodities are transshipped from specific supply nodes to the corresponding demand nodes through the arcs of an underlying capacity network. The maximum flow over time problem concerns to maximize the sum of commodity flows in a given time horizon. It becomes the earliest arrival flow problem if it maximizes the flow at each time step. The earliest arrival transshipment problem is the one that satisfies specified supplies and demands. These flow over time problems are computationally hard. By reverting the orientation of lanes towards the demand nodes, the outbound lane capacities can be increased. We introduce a partial lane reversal approach in the class of multicommodity flow problems. Moreover, a polynomial-time algorithm for the maximum static flow problem and pseudopolynomial algorithms for the earliest arrival transshipment and maximum dynamic flow problems are presented. Also, an approximation solution to the latter problem is obtained in polynomial-time.

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.

scholarly journals A Multi-Commodity Flow Problem for Fair Resource Allocation in Multi-Path Video Delivery Networks

2020 ◽  
Vol 53 (2) ◽  
pp. 7386-7391
Author(s):  
Luca De Cicco ◽  
Gioacchino Manfredi ◽  
Vittorio Palmisano ◽  
Saverio Mascolo
Keyword(s):  
Resource Allocation ◽  
Flow Problem ◽  
Video Delivery ◽  
Commodity Flow ◽  
Delivery Networks

On the integral plane two-commodity flow problem

1992 ◽  
Vol 11 (3) ◽  
pp. 135-139 ◽  
Author(s):  
Frieda Granot ◽  
Michal Penn
Keyword(s):  
Flow Problem ◽  
Commodity Flow ◽  
Integral Plane

scholarly journals Marking Vertices to Find Graph Isomorphism Mapping Based on Continuous-Time Quantum Walk

Entropy ◽  
2018 ◽  
Vol 20 (8) ◽  
pp. 586 ◽  
Author(s):  
Xin Wang ◽  
Yi Zhang ◽  
Kai Lu ◽  
Xiaoping Wang ◽  
Kai Liu
Keyword(s):  
Polynomial Time ◽  
Continuous Time ◽  
Graph Isomorphism ◽  
Quantum Walk ◽  
Isomorphism Problem ◽  
Quantum Walks ◽  
Regular Graphs ◽  
Structure Preserving ◽  
Topological Structures ◽  
Time Quantum

The isomorphism problem involves judging whether two graphs are topologically the same and producing structure-preserving isomorphism mapping. It is widely used in various areas. Diverse algorithms have been proposed to solve this problem in polynomial time, with the help of quantum walks. Some of these algorithms, however, fail to find the isomorphism mapping. Moreover, most algorithms have very limited performance on regular graphs which are generally difficult to deal with due to their symmetry. We propose IsoMarking to discover an isomorphism mapping effectively, based on the quantum walk which is sensitive to topological structures. Firstly, IsoMarking marks vertices so that it can reduce the harmful influence of symmetry. Secondly, IsoMarking can ascertain whether the current candidate bijection is consistent with existing bijections and eventually obtains qualified mapping. Thirdly, our experiments on 1585 pairs of graphs demonstrate that our algorithm performs significantly better on both ordinary graphs and regular graphs.

scholarly journals Multi-Agent Path Finding with Deadlines

2018 ◽  
Author(s):  
Hang Ma ◽  
Glenn Wagner ◽  
Ariel Felner ◽  
Jiaoyang Li ◽  
T. K. Satish Kumar ◽  
...  
Keyword(s):  
Flow Problem ◽  
Search Algorithms ◽  
The Other ◽  
Path Finding ◽  
Combinatorial Search ◽  
Programming Formulation ◽  
Commodity Flow ◽  
Linear Programming Formulation ◽  
Multi Agent ◽  
Integer Linear Programming Formulation

We formalize Multi-Agent Path Finding with Deadlines (MAPF-DL). The objective is to maximize the number of agents that can reach their given goal vertices from their given start vertices within the deadline, without colliding with each other. We first show that MAPF-DL is NP-hard to solve optimally. We then present two classes of optimal algorithms, one based on a reduction of MAPF-DL to a flow problem and a subsequent compact integer linear programming formulation of the resulting reduced abstracted multi-commodity flow network and the other one based on novel combinatorial search algorithms. Our empirical results demonstrate that these MAPF-DL solvers scale well and each one dominates the other ones in different scenarios.

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