Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Steiner Forest Orientation Problems   We consider connectivity problems with orientation constraints. Given a
directed graph $D$ and a collection of ordered node pairs $P$ let $P[D]=\{(u,v)
\in P: D {contains a} uv{-path}}$. In the {\sf Steiner Forest Orientation}
problem we are given an undirected graph $G=(V,E)$ with edge-costs and a set $P
\subseteq V \times V$ of ordered node pairs. The goal is to find a minimum-cost
subgraph $H$ of $G$ and an orientation $D$ of $H$ such that $P[D]=P$. We give a
4-approximation algorithm for this problem.
  In the {\sf Maximum Pairs Orientation} problem we are given a graph $G$ and a
multi-collection of ordered node pairs $P$ on $V$. The goal is to find an
orientation $D$ of $G$ such that $|P[D]|$ is maximum. Generalizing the result
of Arkin and Hassin [DAM'02] for $|P|=2$, we will show that for a mixed graph
$G$ (that may have both directed and undirected edges), one can decide in
$n^{O(|P|)}$ time whether $G$ has an orientation $D$ with $P[D]=P$ (for
undirected graphs this problem admits a polynomial time algorithm for any $P$,
but it is NP-complete on mixed graphs). For undirected graphs, we will show
that one can decide whether $G$ admits an orientation $D$ with $|P[D]| \geq k$
in $O(n+m)+2^{O(k\cdot \log \log k)}$ time; hence this decision problem is
fixed-parameter tractable, which answers an open question from Dorn et al.
[AMB'11]. We also show that {\sf Maximum Pairs Orientation} admits ratio
$O(\log |P|/\log\log |P|)$, which is better than the ratio $O(\log n/\log\log
n)$ of Gamzu et al. [WABI'10] when $|P|<n$.
  Finally, we show that the following node-connectivity problem can be solved
in polynomial time: given a graph $G=(V,E)$ with edge-costs, $s,t \in V$, and
an integer $\ell$, find a min-cost subgraph $H$ of $G$ with an orientation $D$
such that $D$ contains $\ell$ internally-disjoint $st$-paths, and $\ell$
internally-disjoint $ts$-paths.

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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
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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: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: nlin
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The categories of this paper are: math
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The categories of this paper are: physics
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The categories of this paper are: hep-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas