Compact Conformal Map for Greedy Routing in Wireless Mobile Sensor Networks

Li, Siming; Zeng, Wei; Zhou, Dengpan; Gu, Xianfeng; Gao, Jie

doi:10.1109/tmc.2015.2475752

Cited by 10 publications

(5 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Unfortunately, greedy strategies like Compass routing [4] fail for graphs with radio holes, i.e., they might get stuck at a dead end. This can be avoided with the help of suitable virtual coordinates for the nodes (e.g., [14]), but computing these is quite expensive. Instead, Kuhn et al [13] proposed GOAFR, a routing strategy that uses a combination of greedy and face routing, which can find paths with quadratic competitiveness [13].…”

Section: Related Workmentioning

confidence: 99%

Competitive Routing in Hybrid Communication Networks

Jung

Kolb

Scheideler

et al. 2019

Algorithms for Sensor Systems

View full text Add to dashboard Cite

Routing is a challenging problem for wireless ad hoc networks, especially when the nodes are mobile and spread so widely that in most cases multiple hops are needed to route a message from one node to another. In fact, it is known that any online routing protocol has a poor performance in the worst case, in a sense that there is a distribution of nodes resulting in bad routing paths for that protocol, even if the nodes know their geographic positions and the geographic position of the destination of a message is known. The reason for that is that radio holes in the ad hoc network may require messages to take long detours in order to get to a destination, which are hard to find in an online fashion.In this paper, we assume that the wireless ad hoc network can make limited use of long-range links provided by a global communication infrastructure like a cellular infrastructure or a satellite in order to compute an abstraction of the wireless ad hoc network that allows the messages to be sent along near-shortest paths in the ad hoc network. We present distributed algorithms that compute an abstraction of the ad hoc network in O log 2 n time using long-range links, which results in c-competitive routing paths between any two nodes of the ad hoc network for some constant c if the convex hulls of the radio holes do not intersect. We also show that the storage needed for the abstraction just depends on the number and size of the radio holes in the wireless ad hoc network and is independent on the total number of nodes, and this information just has to be known to a few nodes for the routing to work. ACM Subject Classification C.2.4 Distributed SystemsThroughout this paper, we consider V ⊂ R 2 to be a set of nodes in the Euclidean plane with unique IDs (e.g., phone numbers), where |V | = n. For any given pair of nodes u = (u x , u y ), v = (v x , v y ), we denote the Euclidean distance between u and v by ||uv|| =We model our cell phone network as a hybrid directed graph H = (V, E, E AH ) where the node set V represents the set of cell phones, an edge (v, w) is in E whenever v knows the phone number (or simply ID) of w, and an edge (v, w) ∈ E is also in the ad hoc edge set E AH whenever v can send a message to w using its Wifi interface. For all edges (v, w) ∈ E \ E AH , v can only use a long-range link to directly send a message to w. We adopt the unit disk graph model for the edges in E AH .Definition 1. For any point set V ⊆ R 2 the Unit Disk Graph of V , UDG (V ), is a bi-directed graph that contains all edges (u, v) with ||uv|| ≤ 1. C V I T 2 0 1 6

show abstract

Section: Related Workmentioning

confidence: 99%

Competitive Routing in Hybrid Communication Networks

Jung

Kolb

Scheideler

et al. 2019

Algorithms for Sensor Systems

View full text Add to dashboard Cite

show abstract

“…It was also used in [8] for routing in a mobile network and to avoid local minimum solutions by encoding the map of the network domain to virtual coordinates of the canonical domain. To the best knowledge of the authors, the work presented in this paper is the first to apply canonical domains in EC environments.…”

Section: Related Workmentioning

confidence: 99%

“…In the second step, using mapping functions (6) and (7), which map every point of the physical domain to its corresponding one in the canonical domain, we obtain the positions of signaling messages (i.e., data) in the canonical domain. In the third step, due to the uniform nature of the canonical domain, we divide the canonical domain in rectangle tiles using Equations (8) and (9), which map every point of the canonical domain to its corresponding one in the physical domain, and using the argmin function (18), which determines how much resources are needed in the given rectangle tile. This results in positioning the VMs that could fulfill the requests generated in each tile of the canonical domain.…”

Section: Algorithm Of the Core Function Of Cdsp-fmentioning

confidence: 99%

“…This results in positioning the VMs that could fulfill the requests generated in each tile of the canonical domain. In the fourth step, we apply equations (8) and (9) to obtain the positions of generated VMs in the physical domain. In the last step, using the Voronoi diagram (See Equation (19) which determines how the VM clusters for ECs are defined, and Equations (20), (21), and (22) which measure the Haversine distance between VM positions in the physical domain for the Voronoi diagram), we allocate the needed VMs to their corresponding ECs in place.…”

Section: Algorithm Of the Core Function Of Cdsp-fmentioning

confidence: 99%

See 1 more Smart Citation

Conformal Mapping for Optimal Network Slice Planning Based on Canonical Domains

Laghrissi

Taleb

Bagaa

2018

IEEE J. Select. Areas Commun.

View full text Add to dashboard Cite

The evolution towards 5G consists of managing highly dynamic networks and making decisions related to the provisioning of networks in an as-a-service and cost-aware fashion. This is translated by 5G verticals that are dedicated to specific services, applications, or use cases fulfilling the constant demand of vertical industries. In this vein, to achieve the high-level goals defined by operators and service providers, and to answer to the elasticity and low-latency specifications of the upcoming 5G mobile system, the optimal placement of virtual network functions must cope with the non-uniform service demands and the irregular nature of network topologies. This paper addresses this issue by mapping the non-uniform distribution of signaling messages in the physical domain to a new uniform environment (i.e., canonical domain) whereby the placement of core functions is more feasible and efficient by means of Schwartz-Christoffel conformal mappings. The experimentation results, compared to some baseline approaches, have proven the efficiency of the conformal mapping based placement in allocating the virtual resources (i.e., virtual CPU and virtual storage) with regard to the optimal end-to-end delay, cost and activated virtual machines. Another interesting contribution is that all placement decisions are based on a realistic spatio-temporal user-centric model, which defines both the mobility of user equipments and the underlying service usage.

show abstract

“…We briefly review the literature on computing angle-preserving or conformal maps, which play a crucial role in the initialization of our solver-for a more extensive discussion, see Gu & Yau [2008]. In computer graphics, conformal [Crane et al 2011;Vaxman et al 2015], and layout of sensor networks [Li et al 2013]. In architectural geometry, conformal maps have been used for designing circle and sphere packings [Schiftner et al 2009] and paneling layouts [Röhrig et al 2014] on freeform surfaces.…”

Section: Related Workmentioning

confidence: 99%

Beyond developable

Crane²,

et al. 2016

View full text Add to dashboard Cite

Introducing a regular pattern of slits turns inextensible, but flexible sheet material into an auxetic material that can locally expand in an approximately uniform way. This modified deformation behavior allows the material to assume complex double-curved shapes. The shoe model has been fabricated from a single piece of metallic material using a new interactive rationalization method based on conformal geometry and global, non-linear optimization. Thanks to our global approach, the 2D layout of the material can be computed such that no discontinuities occur at the seam. The center zoom shows the region of the seam, where one row of triangles is doubled to allow for easy gluing along the boundaries. The base is 3D printed.

show abstract

Compact Conformal Map for Greedy Routing in Wireless Mobile Sensor Networks

Cited by 10 publications

References 28 publications

Competitive Routing in Hybrid Communication Networks

Competitive Routing in Hybrid Communication Networks

Conformal Mapping for Optimal Network Slice Planning Based on Canonical Domains

Beyond developable

Contact Info

Product

Resources

About