Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Flow-Cut Gaps for Integer and Fractional Multiflows   Consider a routing problem consisting of a demand graph H and a supply graph
G. If the pair obeys the cut condition, then the flow-cut gap for this instance
is the minimum value C such that there is a feasible multiflow for H if each
edge of G is given capacity C. The flow-cut gap can be greater than 1 even when
G is the (series-parallel) graph K_{2,3}. In this paper we are primarily
interested in the "integer" flow-cut gap. What is the minimum value C such that
there is a feasible integer valued multiflow for H if each edge of G is given
capacity C? We conjecture that the integer flow-cut gap is quantitatively
related to the fractional flow-cut gap. This strengthens the well-known
conjecture that the flow-cut gap in planar and minor-free graphs is O(1) to
suggest that the integer flow-cut gap is O(1). We give several results on
non-trivial special classes of graphs supporting this conjecture and further
explore the "primal" method for understanding flow-cut gaps. Our results
include:
  - Let G be obtained by series-parallel operations starting from an edge st,
and consider orienting all edges in G in the direction from s to t. A demand is
compliant if its endpoints are joined by a directed path in the resulting
oriented graph. If the cut condition holds for a compliant instance and G+H is
Eulerian, then an integral routing of H exists.
  - The integer flow-cut gap in series-parallel graphs is 5. We also give an
explicit class of instances that shows via elementary calculations that the
flow-cut gap in series-parallel graphs is at least 2-o(1); this simplifies the
proof by Lee and Raghavendra.
  - The integer flow-cut gap in k-Outerplanar graphs is c^{O(k)} for some fixed
constant c.
  - A simple proof that the flow-cut gap is O(\log k^*) where k^* is the size
of a node-cover in H; this was previously shown by G\"unl\"uk via a more
intricate proof.

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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
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The categories of this paper are: q-alg
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The categories of this paper are: econ
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The categories of this paper are: acc-phys
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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: nlin
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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin