We consider the ad-hoc networks consisting of n wireless nodes that are located on the plane. Any two given nodes are called neighbors if they are located within a certain distance (communication range) from one another. A given node can be directly connected to any one of its neighbors, and picks its connections according to a unique topology control algorithm that is available at every node. Given that each node knows only the indices (unique identification numbers) of its one and two-hop neighbors, we identify an algorithm that preserves connectivity and can operate without the need of any synchronization among nodes. Moreover, the algorithm results in a sparse graph with at most 5n edges and a maximum node degree of 10. Existing algorithms with the same promises further require neighbor distance and/or direction information at each node. We also evaluate the performance of our algorithm for random networks. In this case, our algorithm provides an asymptotically connected network with n(1+o(1)) edges with a degree less than or equal to 6 for 1-o(1) fraction of the nodes. We also introduce another asynchronous connectivity-preserving algorithm that can provide an upper bound as well as a lower bound on node degrees.
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Multilayer Network Clarifies Prevailing Water Consumption Telecouplings in the United States
Virtual water flows are used to map the indirect water consumption connections implied by the supply chain of a city, region, or country. This information can be used to manage supply chains to achieve environmental policy objectives and mitigate environmental risks to critical supply chains. A limitation of prior work is that these flows are typically analyzed using monolayer networks, which ignores crucial intersectoral or interlayer couplings. Here, we use a multilayer network to account for such couplings when analyzing blue virtual water flows in the United States. Our multilayer network consists of 115 different regions (nodes), covering the entire conterminous United States; 41 coupled economic sectors (layers); and ∼2 × 107possible links. To analyze the multilayer network, we focus on three fundamental network properties: topological connectivity, mesoscale structure, and node centrality. The network has a high connectivity, with each node being on average connected to roughly 2/3 of the network's nodes. Interlayer flows are a major driver of connectivity, representing ∼54% of all the network's connections. Five different groups of tightly connected nodes (communities) characterize the network. Each community represents a preferred spatial mode of long‐range virtual water interaction within the United States. We find that large (populous) cities have a stronger influence than small ones on network functioning because they attract and recirculate more virtual water through their supply chains. Our results also highlight differences between the multilayer and monolayer virtual water network, which overall show that the former provides a more realistic representation of virtual water flows.
more » « less- Award ID(s):
- 1639529
- NSF-PAR ID:
- 10367892
- Publisher / Repository:
- DOI PREFIX: 10.1029
- Date Published:
- Journal Name:
- Water Resources Research
- Volume:
- 57
- Issue:
- 7
- ISSN:
- 0043-1397
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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