Exact and Approximate Digraph Bandwidth

Abstract

In this paper, we introduce a directed variant of the classical Bandwidthproblem and study it from the view-point of moderately exponential time algorithms, both exactly and approximately. Motivated by the definitions of the directed variants of the classical Cutwidth and Pathwidth problems, we define Digraph Bandwidth as follows. Given a digraph D and an ordering σ of its vertices, the digraph bandwidth of σ with respect to D is equal to the maximum value of σ(v)-σ(u) over all arcs (u,v) of D going forward along σ (that is, when σ(u) 0, we can find an ordering whose digraph bandwidth is at most (1+ϵ) times the optimal digraph bandwidth, in time O⋆(4n·(⌈4/ϵ⌉)n).