Macroscopic Network Circulation for Planar Graphs
| Autor: | Fariba Ariaei, Zahra Askarzadeh, Yongxin Chen, Tryphon T. Georgiou |
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| Rok vydání: | 2022 |
| Předmět: |
FOS: Computer and information sciences
05C10 57M15 05C81 Control and Optimization Discrete Mathematics (cs.DM) Optimization and Control (math.OC) Computer Networks and Communications Control and Systems Engineering Signal Processing FOS: Mathematics Mathematics - Combinatorics Combinatorics (math.CO) Mathematics - Optimization and Control Computer Science - Discrete Mathematics |
| Zdroj: | IEEE Transactions on Control of Network Systems. 9:1840-1850 |
| ISSN: | 2372-2533 |
| Popis: | The analysis of networks, aimed at suitably defined functionality, often focuses on partitions into subnetworks that capture desired features. Chief among the relevant concepts is a 2-partition, that underlies the classical Cheeger inequality, and highlights a constriction (bottleneck) that limits accessibility between the respective parts of the network. In a similar spirit, the purpose of the present work is to introduce a new concept of maximal global circulation and to explore 3-partitions that expose this type of macroscopic feature of networks. Herein, graph circulation is motivated by transportation networks and probabilistic flows (Markov chains) on graphs. Our goal is to quantify the large-scale imbalance of network flows and delineate key parts that mediate such global features. While we introduce and propose these notions in a general setting, in this paper, we only work out the case of planar graphs. We explain that a scalar potential can be identified to encapsulate the concept of circulation, quite similarly as in the case of the curl of planar vector fields. Beyond planar graphs, in the general case, the problem to determine global circulation remains at present a combinatorial problem. 20 pages, 11 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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