Calculating with Relations for Graph Algorithmics

Relations, graphs and programs

Much emphasis has been placed in recent years on deriving or calculating programs rather than proving them correct. Adequate calculational frame­ works are needed to support such an approach. This thesis explores the use of a calculus of binary relations to express and reason about graph-theoretical concepts in the context of program construction. Since graphs playa promi­ nent role in algorith...

A Parameterized Route to Exact Puzzles: Breaking the 2-Barrier for irredundance

The lower and the upper irredundance numbers of a graph G, denoted ir(G) and IR(G) respectively, are conceptually linked to domination and independence numbers and have numerous relations to other graph parameters. It is a long-standing open question whether determining these numbers for a graph G on n vertices admits exact algorithms running in time less than the trivial Ω(2) enumeration barri...

Breaking the 2^n-Barrier for Irredundance: A Parameterized Route to Solving Exact Puzzles

The lower and the upper irredundance numbers of a graph G, denoted ir(G) and IR(G) respectively, are conceptually linked to domination and independence numbers and have numerous relations to other graph parameters. It is a long-standing open question whether determining these numbers for a graph G on n vertices admits exact algorithms running in time less than the trivial Ω(2) enumeration barri...

A Parameterized Route to Exact Puzzles: Breaking the 2n-Barrier for Irredundance

The lower and the upper irredundance numbers of a graph G, denoted ir(G) and IR(G) respectively, are conceptually linked to domination and independence numbers and have numerous relations to other graph parameters. It is a long-standing open question whether determining these numbers for a graph G on n vertices admits exact algorithms running in time less than the trivial Ω(2) enumeration barri...

Parameterized Algorithmics: A Graph-Theoretic Approach