scholarly journals Low-diameter topic-based pub/sub overlay network construction with minimum–maximum node degree

2021 ◽  
Vol 7 ◽  
pp. e538
Author(s):  
Semih Yumusak ◽  
Sina Layazali ◽  
Kasim Oztoprak ◽  
Reza Hassanpour
Keyword(s):  
Heuristic Algorithm ◽  
Maximum Degree ◽  
Overlay Networks ◽  
Overlay Network ◽  
Node Degree ◽  
Network Construction ◽  
Network Diameter ◽  
Constant Diameter ◽  
Minimum Number ◽  
Run Up

In the construction of effective and scalable overlay networks, publish/subscribe (pub/sub) network designers prefer to keep the diameter and maximum node degree of the network low. However, existing algorithms are not capable of simultaneously decreasing the maximum node degree and the network diameter. To address this issue in an overlay network with various topics, we present herein a heuristic algorithm, called the constant-diameter minimum–maximum degree (CD-MAX), which decreases the maximum node degree and maintains the diameter of the overlay network at two as the highest. The proposed algorithm based on the greedy merge algorithm selects the node with the minimum number of neighbors. The output of the CD-MAX algorithm is enhanced by applying a refinement stage through the CD-MAX-Ref algorithm, which further improves the maximum node degrees. The numerical results of the algorithm simulation indicate that the CD-MAX and CD-MAX-Ref algorithms improve the maximum node-degree by up to 64% and run up to four times faster than similar algorithms.

scholarly journals Total Coloring Conjecture for Certain Classes of Graphs

Algorithms ◽  
2018 ◽  
Vol 11 (10) ◽  
pp. 161 ◽  
Author(s):  
R. Vignesh ◽  
J. Geetha ◽  
K. Somasundaram
Keyword(s):  
Chromatic Number ◽  
Maximum Degree ◽  
Line Graph ◽  
Product Line ◽  
Total Coloring ◽  
Lexicographic Product ◽  
Total Chromatic Number ◽  
Minimum Number ◽  
Total Coloring Conjecture

A total coloring of a graph G is an assignment of colors to the elements of the graph G such that no two adjacent or incident elements receive the same color. The total chromatic number of a graph G, denoted by χ ′ ′ ( G ) , is the minimum number of colors that suffice in a total coloring. Behzad and Vizing conjectured that for any graph G, Δ ( G ) + 1 ≤ χ ′ ′ ( G ) ≤ Δ ( G ) + 2 , where Δ ( G ) is the maximum degree of G. In this paper, we prove the total coloring conjecture for certain classes of graphs of deleted lexicographic product, line graph and double graph.

scholarly journals Distinct Distances in Graph Drawings

10.37236/831 ◽  
2008 ◽  
Vol 15 (1) ◽  
Author(s):  
Paz Carmi ◽  
Vida Dujmović ◽  
Pat Morin ◽  
David R. Wood
Keyword(s):  
Maximum Degree ◽  
Combinatorial Geometry ◽  
Complete Graphs ◽  
Bounded Degree ◽  
Cartesian Products ◽  
Bounded Treewidth ◽  
Line Drawings ◽  
Straight Line ◽  
Minimum Number ◽  
Complete Bipartite Graphs

The distance-number of a graph $G$ is the minimum number of distinct edge-lengths over all straight-line drawings of $G$ in the plane. This definition generalises many well-known concepts in combinatorial geometry. We consider the distance-number of trees, graphs with no $K^-_4$-minor, complete bipartite graphs, complete graphs, and cartesian products. Our main results concern the distance-number of graphs with bounded degree. We prove that $n$-vertex graphs with bounded maximum degree and bounded treewidth have distance-number in ${\cal O}(\log n)$. To conclude such a logarithmic upper bound, both the degree and the treewidth need to be bounded. In particular, we construct graphs with treewidth $2$ and polynomial distance-number. Similarly, we prove that there exist graphs with maximum degree $5$ and arbitrarily large distance-number. Moreover, as $\Delta$ increases the existential lower bound on the distance-number of $\Delta$-regular graphs tends to $\Omega(n^{0.864138})$.

scholarly journals Node clone detection using a stable overlay network

2020 ◽  
Vol 10 (1) ◽  
pp. 316
Author(s):  
Balika J. Chelliah ◽  
M. S. Antony Vigil ◽  
M. S. Bennet Praba
Keyword(s):  
Wireless Sensor Networks ◽  
Overlay Networks ◽  
Overlay Network ◽  
Sensor Nodes ◽  
Wireless Sensor ◽  
Security Level ◽  
Clone Detection ◽  
Data Prediction ◽  
High Security Level ◽  
Balanced Network

Wireless sensor networks consist of number of sensor nodes widely distributed in particular region to communicate and sharing the environmental information and also these data’s are stored in central location for further data prediction. Such nodes are susceptible to cloning attack where the adversary captures a node, replicates with the same identity as that of the captured node and deploys the clone back into the network, causing severe harm to the network. Hence to thwart such attacks, a distributed detection protocol is used with initiator-observer-inspector roles assigned randomly for the nodes to witness the clone and thereby broadcast the evidence through a balanced overlay network. Use of such balanced network provides high security level and reduces the communication cost when compared to other overlay networks with a reasonably less storage consumption.

Handoff Cost Minimization and Planning of Heterogeneous Integrated Overlay Networks

2012 ◽  
pp. 49-64
Author(s):  
Ayan Paul ◽  
Madhubanti Maitra ◽  
Swarup Mandal ◽  
Samir Kumar Sadhukhan
Keyword(s):  
Overlay Networks ◽  
Cost Minimization ◽  
Cost Effective ◽  
Overlay Network ◽  
Vertical Handoff ◽  
Planning Problem ◽  
Network Resources ◽  
Planning Approach ◽  
Technology Market ◽  
The Cost

The wireless technology market has witnessed a complete paradigm shift as multiple standards and protocols are emerging almost every day. Each and every standard has its limitations and merits, which can be either masked or complemented by some other standards. The demands from the service providers are now sky-high and for the complete commercialization, it is expected that even with scarce network resources all kind of services would be provided, especially in a cost effective manner. This burning issue compels a service provider to roll out some integrated wireless networks to exploit the virtues of each. This chapter formulates the planning problem of an overlay network integrating particularly, 3G, WiMAX, and WLAN. The issue of planning is to establish proper connectivity amongst the three network standards which is unique in its nature. In the proposed planning approach, the authors have endeavored to minimize total cost for vertical handoff generated in the overlay network as well as the cost for wire line connection amongst the various network gateways of the overlay hierarchy. In this work, the authors have focused on the initial planning phase. For validating the novel planning problem, the chapter has taken recourse to simulated annealing (SA) and a well cited meta-heuristic H-II. The authors have also presented comparison of the performances of SA and H-II with a variant of distance based planning (DBP) scheme in this domain.

2-distance vertex-distinguishing total coloring of graphs

2018 ◽  
Vol 10 (02) ◽  
pp. 1850018
Author(s):  
Yafang Hu ◽  
Weifan Wang
Keyword(s):  
Chromatic Number ◽  
Maximum Degree ◽  
Simple Graph ◽  
Total Coloring ◽  
Total Chromatic Number ◽  
Minimum Number ◽  
Number Formula ◽  
Proper Total Coloring ◽  
Distance Formula

A [Formula: see text]-distance vertex-distinguishing total coloring of a graph [Formula: see text] is a proper total coloring of [Formula: see text] such that any pair of vertices at distance [Formula: see text] have distinct sets of colors. The [Formula: see text]-distance vertex-distinguishing total chromatic number [Formula: see text] of [Formula: see text] is the minimum number of colors needed for a [Formula: see text]-distance vertex-distinguishing total coloring of [Formula: see text]. In this paper, we determine the [Formula: see text]-distance vertex-distinguishing total chromatic number of some graphs such as paths, cycles, wheels, trees, unicycle graphs, [Formula: see text], and [Formula: see text]. We conjecture that every simple graph [Formula: see text] with maximum degree [Formula: see text] satisfies [Formula: see text].

scholarly journals A Prediction System Using a P2P Overlay Network for a Bus Arrival System

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Ssu-Hsuan Lu ◽  
Yu-Wei Chan
Keyword(s):  
Sensor Networks ◽  
Overlay Networks ◽  
Overlay Network ◽  
Wireless Sensor ◽  
Rail Transportation ◽  
Transit Systems ◽  
Arrival Times ◽  
Multiple Sensor ◽  
Moving Speed ◽  
P2p Overlay

Along with the evolution of times and the surge of metropolitan populations, government agencies often promote the construction of public transport. Unlike rail transportation or rapid transit systems, it is often difficult to estimate the vehicle arrival times at each station in a bus transportation system due to metropolitan transportation congestion. Traffic status is often monitored using wireless sensor networks (WSNs). However, WSNs are always separated from one another spatially. Recent studies have considered the connection of multiple sensor networks. This study considers a combination view of peer-to-peer (P2P) overlay networks and WSN architecture to predict bus arrival times. Each bus station, which is also a P2P overlay peer, is connected in a P2P overlay network. A sensor installed in each bus can receive data via peers to obtain the moving speed of a bus. Then, each peer can exchange its data to predict bus arrival times at bus stations. This method can considerably increase the accuracy with which bus arrival times can be predicted and can provide traffic status with high precision. Furthermore, these data can also be used to plan new bus routes according to the information gathered.

scholarly journals Balanced Scheduling of School Bus Trips using a Perfect Matching Heuristic

2018 ◽  
Vol 2672 (48) ◽  
pp. 1-11 ◽  
Author(s):  
Ali Shafahi ◽  
Sanaz Aliari ◽  
Ali Haghani
Keyword(s):  
Heuristic Algorithm ◽  
School Setting ◽  
Mixed Integer ◽  
Scheduling Problem ◽  
School Bus ◽  
Heuristic Solution ◽  
Mip Model ◽  
Bus Scheduling ◽  
Minimum Number ◽  
The Cost

In the school bus scheduling problem, the main contributing factor to the cost is the number of buses needed for the operations. However, when subcontracting the pupils’ transportation, unbalanced tours can increase the costs significantly as the lengths of some tours can exceed the daily fixed driving goal and will result in over-hour charges. This paper proposes a mixed integer programming (MIP) model and a matching-based heuristic algorithm to solve the “balanced” school bus scheduling problem with fixed start times in a multi-school setting. The heuristic solution always has the minimum number of buses as it starts with a minimal number of tours and does not alter the number of tours during its balancing stage. The effectiveness of the heuristic is tested by comparing its solutions with results from solving the MIP using commercial solvers whenever solvers could find a good solution. To illustrate the performance of the MIP and the heuristic, 11 problems were examined with different numbers of trips which are all based on two real-world problems: a California case study with 54 trips and the Howard County Public School System with 994 trips. Our numerical results indicate the proposed heuristic algorithm can find reasonable solutions in a significantly shorter time. The balanced solutions of our algorithm can save up to 16% of school bus operation costs compared with the best solution found by solvers from optimizing the MIP model after 40 hours. The balancing stage of the heuristic decreases the standard deviation of the tour durations by up to 47%.

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