Algorithms for generating all possible spanning trees of a simple undirected connected graph: an extensive review

Chakraborty, Maumita; Chowdhury, Sumon; Chakraborty, Joymallya; Mehera, Ranjan; Pal, Rajat Kumar

doi:10.1007/s40747-018-0079-7

Cited by 28 publications

(24 citation statements)

References 18 publications

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“…1) Assign the IP and broadcast the address to an SDN controller after its initialization. 2) Find all the routing paths by STP (all possible STs [34]), Distance-based MST (using MST Function), Hop-based MST (using MST Function) according to selected spanning tree protocol and then put them into the routing path list. 3) Initially the Path Estimate Lifetime (PELT) would be zero.…”

Section: ) Algorithm For Sdn Controllermentioning

confidence: 99%

Optimizing the Lifetime of Software Defined Wireless Sensor Network via Reinforcement Learning

et al. 2021

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Section: ) Algorithm For Sdn Controllermentioning

confidence: 99%

Optimizing the Lifetime of Software Defined Wireless Sensor Network via Reinforcement Learning

et al. 2021

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“…In (45), the search space consists of all the spanning trees of a simple undirected connected graph on N vertices [44], the size of which is determined by Cayley's Formula [45].…”

Section: User Pairing Strategymentioning

confidence: 99%

Efficient Detection Scheme for Physical-Layer Network Coding in Multiway Relay Channels

Chang

Champagne

2019

IEEE Access

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In this paper, we propose a novel scheme for physical-layer network coding (PNC) in multiway relay channels (MWRC) from the perspective of sequential multiuser detection. We consider an uplink MWRC scenario where N users, each equipped with a single antenna, simultaneously transmit their signal to a relay equipped with K antennas (K < N ). Extraction of the network codes from the superimposed user signals at the relay node is formulated as an under-determined linear system. To solve this problem with low decoding complexity, the proposed method combines successive interference cancellation (SIC) with Babai estimation for regularized integer least squares (ILS). Specifically, SIC decoding is first employed to detect a selected subset of stronger user signals and remove their interfering effects. Babai estimation is then applied to extract the remaining user signals, which is formulated as an ILS problem with reduced dimension. We develop a power allocation scheme to enhance the performance of both SIC and ILS steps, and discuss an optimal user pairing strategy based on the average decoding error probability. Numerical results demonstrate the performance improvement of the proposed method in extracting network codes from multiple superimposed user signals.INDEX TERMS Babai estimation, multiway relay channel (MWRC), physical-layer network coding (PNC), successive interference cancellation (SIC).

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“…However, in case of large graphs, this theorem becomes impractical due to the determinant of a large matrix. That is why many combinatorial methods have been developed for some graph families [13][14][15]. The remedy for this problem was to develop simple techniques based on suppression deletion and decomposition of the graph to sub-graphs and treat each sub-graph separately [1,2].…”

Section: Introductionmentioning

confidence: 99%

Computing the number of spanning trees in the Wheel multiple graph

Khattabi¹

2019

IJATCSE

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The number of spanning trees in a network relevant to several networks aspects, namely their topological and dynamic properties such as their reliability. Generally, this number can be obtained by the well-known Matrix Tree Theorem. However, computing the number of spanning trees in a network using this method is computationally demanding specially for a large network, which leads us to investigate the number of spanning trees in planar graphs. In this paper, we propose an efficient method to find exact formulas for counting the number of spanning trees in a general type of the multiple planar wheel graph.

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Algorithms for generating all possible spanning trees of a simple undirected connected graph: an extensive review

Cited by 28 publications

References 18 publications

Optimizing the Lifetime of Software Defined Wireless Sensor Network via Reinforcement Learning

Optimizing the Lifetime of Software Defined Wireless Sensor Network via Reinforcement Learning

Efficient Detection Scheme for Physical-Layer Network Coding in Multiway Relay Channels

Computing the number of spanning trees in the Wheel multiple graph

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