Double-Change Covering Designs with Block Size k = 4

Author

Nirosh Tharaka Sandakelum Gangoda Gamachchige, Southern Illinois University CarbondaleFollow

Date of Award

8-1-2017

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

McSorley, John

Abstract

A double-change covering design (dccd) is an ordered set of blocks with block size k is an ordered collection of b blocks, B = {B1,B2, · · · ,Bb}, each an unordered subset of k distinct elements from [v] = {1, 2, · · · , v}, which obey: (1) each block differs from the previous block by two elements, and, (2) every unordered pair of [v] appears in at least one block. The object is to minimize b for a fixed v and k. Tight designs are those in which each pair is covered exactly once. We present constructions of tight dccd’s for arbitrary v when k = 2 and minimal constructions for v <= 20 when k = 4. A general, but not minimal, method is presented to construct circular dccd for arbitrary v when k = 4.