ON THE EMBEDDING OF GROUPS AND DESIGNS IN A DIFFERENCE BLOCK DESIGN

A difference BIBD is a balanced incomplete block design on a group which isconstructed by transferring a regular perfect difference system by a subgroup of its point set. There is an obvious bijection between these BIBDs and some copies of their point sets as two sets. In this paper, we investigate the algebraic structure of these block designs by definning a group-isomorphism between them and their point sets. It has done by defning some relations between the independent-graphs of difference BIBDs and some Cayley graphs of their point sets. It is shown that some Cayley graphs are embedded in the independent-graph of difference BIBDs as a spanning sub-graphs. Due to find these relations, we find out a configuration ordering on these BIBDs, also we achieve some results about the classification of these BIBDs. All in this paper are on difference BIBDs with even numbers of the points.

Finite Euclidean Geometry Approach for Constructing Balanced Incomplete Block Design (BIBD)

In block design, construction of Balanced Incomplete Block Design (BIBD) remained an unsolved problem in combinatorial design; also various construction techniques have been introduced to build the elements of BIBDs for specific parameters; no general method has been proposed to find a suitable structure for BIBDs. This paper aim at employing Finite Euclidean Geometry FEG (N,s) of N – dimensional space to construct balanced incomplete block design (BIBD). Also geometrical construction of FEG (2,2) BIBDs has been made. The results show that this technique proved a better method for constructing BIBD than other methods in terms of estimation of parameters to build the design structure.

Remarks about a construction method for D-optimal chemical balance weighing designs

SummaryThis paper presents some constructions of regular D-optimal weighing designs based on the incidence matrices of a balanced incomplete block design, balanced bipartite weighing design and ternary balanced block design. We determine optimality conditions and relations between the parameters of the design, and give an example.

Prime-number-assisted block-based neighbor discovery protocol in wireless sensor networks

During the initial deployment time, wireless sensors continually search their neighbors. The neighbor discovery is not an one-time event because the network topology can be changed anytime due to node mobility and failure. The neighbor discovery protocol helps sensor nodes to find neighboring sensors within their communication range. This study proposes a novel neighbor discovery protocol called the prime-number-assisted block-based neighbor discovery protocol, which intelligently changes the sensor schedules based on the greater common divisor of two sensors’ discovery cycle lengths. For example, for two sensors whose duty cycles are different, if the lengths of their discovery schedules are relatively prime, the prime-number-assisted block-based neighbor discovery protocol simply uses the balanced incomplete block design–based neighbor discovery protocol without adding any additional active slots; otherwise, it changes the original balanced incomplete block design–based schedule using a prime number. In this study, we compare the performances of prime-number-assisted block-based neighbor discovery protocol and other recently proposed neighbor discovery protocols (U-Connect, Disco, SearchLight, and Hedis) using a TOSSIM simulator. The experimental results confirm the superiority of prime-number-assisted block-based neighbor discovery protocol over other neighbor discovery protocols in terms of discovery latency and energy consumptions.