Flow-Cut Gaps for Integer and Fractional Multiflows

Consider a routing problem instance consisting of a demand graph H = (V, E(H)) and a supply graph G = (V, E(G)). If the pair obeys the cut condition, then the flow-cut gap for this instance is the minimum value C such that there exists a feasible multiflow for H if each edge of G is given capacity C. It is wellknown that the flow-cut gap may be greater than 1 even in the case where G is the (series-parallel) graph K2,3. In this paper we are primarily interested in the "integer" flow-cut gap. What is the minimum value C such that there exists a feasible integer valued multiflow for H if each edge of G is given capacity C? We formulate a conjecture that states that the integer flow-cut gap is quantitatively related to the fractional flow-cut gap. In particular this strengthens the well-known conjecture that the flow-cut gap in planar and minor-free graphs is O(1) [14] to suggest that the integer flow-cut gap is O(1). We give several technical tools and results on non-trivial s...

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Chandra Chekuri, F. Bruce Shepherd, Christophe Weibel
• Keywords: CORR 2010, Education, Flow-cut Gap, Integer Flow-cut Gap, Minimum Value