Approximations for the Maximum Acyclic Subgraph Problem

Abstract Given a directed graph G = (V,A), the maximum acyclic subgraph problem is to compute a subset, A′, of arcs of maximum size or total weight so that G′ = (V,A′) is acyclic. We discuss several approximation algorithms for this problem. Our main result is an O(|A| + d3max) algorithm that produces a solution with at least a fraction 1 2 +ω( 1 d max ) of the number of arcs in an optimal solution. Here, dmax is the maximum vertex degree in G.

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