Spanner of an undirected graph G = (V, E) is a subgraph which is sparse and yet preserves all-pairs distances approximately. More formally, a spanner with stretch t ∈ N is a subgraph (V, ES), ES ⊆ E such that the distance between any two vertices in the subgraph is at most t times their distance in G. Though G is trivially a t-spanner of itself, the research as well as applications of spanners invariably deal with a t-spanner which has as small number of edges as possible.We present fully dynamic algorithms for maintaining spanners in centralized as well as synchronized distributed environments. These algorithms are designed for undirected unweighted graphs and use randomization in a crucial manner.Our algorithms significantly improve the existing fully dynamic algorithms for graph spanners. The expected size (number of edges) of a t-spanner maintained at each stage by our algorithms matches, up to a poly-logarithmic factor, the worst case optimal size of a t-spanner. The expected amortized time (or messages communicated in distributed environment) to process a single insertion/deletion of an edge by our algorithms is close to optimal. * The results of the preliminary version of this article appeared in ESA 2006 and SODA 2008

Purpose: This paper aims to explore ten years of data on net premiums received and incurred claims of select health insurance companies and compare it with public sector total health insurance. Design/methodology/approach: It is an exploratory paper comparing year-on-year premiums received and incurred claims of health during the period 2011-12 to 2020-21. ( Indian financial year start from April to March). Data has been shown in charts with trend lines without constants. Further, the Compounded Annual Growth Rate ( CAGR) has been calculated using log-linear regression. Findings:  The private sector is in business to earn profits, while the public sector is liberal in remitting the claims. Private-sector businesses earn more premiums than the public sector. However, the private sector’s incurred claims are comparatively much less than the public sector’s. The private sector is increasing business, but public sector growth is falling. The difference between year-on-year net premiums and incurred claims of the public sector is decreasing at 6.95%, but the same is increasing in the private sector at 19.63%. However, it cannot be generalised that the private sector is taking over the public sector business. The public is playing its social responsibility with accountability. However, the private sector aims to earn more earnings.

Abstract: Purpose: To study the hidden factors of suppliers’ and vendors’ relationship in Business to the Business sector in Madhya Pradesh. Design/methodology/approach: For this paper, 10 questions were asked to 856 suppliers of B2B of various products in various cities of Madhya Pradesh. The Relative Importance Index was calculated to rank the variables. The data was later subjected to factor analysis and hidden factors were observed Findings:   Suppliers expect Committed Relationship from their vendors. Suppliers trust their vendors/customers. They are proud to have their customers and in return their buyers trust them. However they face big competition in supplying the goods. Despite their customers (vendors) don't mind minor price changes.  We find our customers loyal to us.  Customers who are more price-sensitive are less loyal. Payment in time is an issue but not relatively important.  The issues like payment in time and skipping orders in between are not important. There is competitive environment, as they are not the only supplier. The important factors are committed relationship and competitive environment. Factor analysis shows that committed relationship explain approximately 36% variances are explained while approximately 14% variances explained by competitive environment. Key Words: B2B, Suppliers, Vendors, Competitive Environment, Important relationship in B2B Paper type:  Empirical Research

No abstract

No abstract