On the Construction of Balanced Incomplete Block Designs Using Lotto Designs

Construction of Balanced Incomplete Block Designs Using Cyclic Shifts

The construction of balanced incomplete block designs is considered using the method of cyclic shifts. An interesting feature of this method is that there is no need to construct the bocks of the actual design to obtain the properties of a design. One can obtain the off-diagonal elements of the concurrence matrix from the sets of shifts with less effort. A catalogue of balanced incomplete block...

Splitting balanced incomplete block designs

Remarks on Balanced Incomplete Block Designs

Proof. Assume the hypothesis and the falsity of either conclusion. Construct matrix A of 2x + 2 rows and 4x+4 columns, with entries + 1 and — 1. The first column contains exclusively +1, and the second column — 1. Set up one-to-one correspondences between rows of A and elements of D ; between columns other than the first two of A and blocks of D. Enter +1 if the element is contained in the bloc...

On Ordinal Covering of Proposals Using Balanced Incomplete Block Designs

A frequently encountered problem in peer review systems is to facilitate pairwise comparisons of a given set of proposals by as few as referees as possible. In [8], it was shown that, if each referee is assigned to review k proposals then n(n-1)/k(k-1) referees are necessary and n(2n-k)/k referees are sufficient to cover all n(n-1)/2 pairs of n proposals. While the upper bound remains withi...

Finding Balanced Incomplete Block Designs with Metaheuristics

This paper deals with the generation of balanced incomplete block designs (BIBD), a hard constrained combinatorial problem with multiple applications. This problem is here formulated as a combinatorial optimization problem (COP) whose solutions are binary matrices. Two different neighborhood structures are defined, based on bit-flipping and position-swapping. These are used within three metaheu...