Review articleMinimax algebra and applications
AbstractWe consider theories of linear and of polynomial algebra, over two scalar systems, often called max-algebra and min-algebra. Here, max-algebra is the system M = (R ∪ {−∞}, ⊛, ⊗) where x ⊛ y = max(x, y) and x ⊛ y = x + y. Min-algebra is the dual system M′ = R ∪ {+∞}, ⊛, ⊗′ with x ⊛′ y = min(x, y) and x ⊗′ y = x + y. Towards the end we also consider minimax algebra, the system M″ = (R ∪ {−∞, +∞}, ⊛, ⊗, ⊛′, ⊗′). Application fields discussed include location problems, machine scheduling, cutting and packing problems, discrete-event systems and path-finding problems.
R.A. Cuninghame-Green
Publication date: 1991/06/14