Smart Bubble Sort:A Novel and Dynamic Variant of Bubble Sort Algorithm

In the present era,a very huge volume of data is being stored in online and offline databases.Enterprise houses,research,medical as well as healthcare organizations,and academic institutions store data in databases and their subsequent retrievals are performed for further processing.Finding the required data from a given database within the minimum possible time is one of the key factors in achieving the best possible performance of any computer-based application.If the data is already sorted,finding or searching is comparatively faster.In real-life scenarios,the data collected from different sources may not be in sorted order.Sorting algorithms are required to arrange the data in some order in the least possible time.In this paper,I propose an intelligent approach towards designing a smart variant of the bubble sort algorithm.I call it Smart Bubble sort that exhibits dynamic footprint:The capability of adapting itself from the average-case to the best-case scenario.It is an in-place sorting algorithm and its best-case time complexity isΩ(n).It is linear and better than bubble sort,selection sort,and merge sort.In averagecase and worst-case analyses,the complexity estimates are based on its static footprint analyses.Its complexity in worst-case is O(n2)and in average-case isΘ(n^(2)).Smart Bubble sort is capable of adapting itself to the best-case scenario from the average-case scenario at any subsequent stages due to its dynamic and intelligent nature.The Smart Bubble sort outperforms bubble sort,selection sort,and merge sort in the best-case scenario whereas it outperforms bubble sort in the average-case scenario.

Improved-Equalized Cluster Head Election Routing Protocol for Wireless Sensor Networks

Throughout the use of the small battery-operated sensor nodes encou-rage us to develop an energy-efficient routing protocol for wireless sensor networks(WSNs).The development of an energy-efficient routing protocol is a mainly adopted technique to enhance the lifetime of WSN.Many routing protocols are available,but the issue is still alive.Clustering is one of the most important techniques in the existing routing protocols.In the clustering-based model,the important thing is the selection of the cluster heads.In this paper,we have proposed a scheme that uses the bubble sort algorithm for cluster head selection by considering the remaining energy and the distance of the nodes in each cluster.Initially,the bubble sort algorithm chose the two nodes with the maximum remaining energy in the cluster and chose a cluster head with a small distance.The proposed scheme performs hierarchal routing and direct routing with some energy thresholds.The simulation will be performed in MATLAB to justify its performance and results and compared with the ECHERP model to justify its performance.Moreover,the simulations will be performed in two scenarios,gate-way-based and without gateway to achieve more energy-efficient results.

Conditional Connectivity of Bubble Sort Graphs

A subset F V（G） is called an Rk-vertex-cut of a graph G if G - F is disconnected and each vertex of G - F has at least k neighbors in G - F. The Rk-vertex-connectivity of G, denoted by κk（G）, is the cardinality of a minimum Rk-vertex-cut of G. Let Bn be the bubble sort graph of dimension n. It is known that κk（Bn） = 2k（n - k - 1） for n _〉 2k and k = 1,2. In this paper, we prove it for k =3 and conjecture that it is true for all k ∈ N. We also prove that the connectivity cannot be more than conjectured.