Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Combinatorial Algorithms for Rooted Prize-Collecting Walks and
  Applications to Orienteering and Minimum-Latency Problems   We consider the rooted prize-collecting walks (PCW) problem, wherein we seek
a collection $C$ of rooted walks having minimum prize-collecting cost, which is
the (total cost of walks in $C$) + (total node-reward of nodes not visited by
any walk in $C$). This problem arises naturally as the Lagrangian relaxation of
both orienteering, where we seek a length-bounded walk of maximum reward, and
the $\ell$-stroll problem, where we seek a minimum-length walk covering at
least $\ell$ nodes. Our main contribution is to devise a simple, combinatorial
algorithm for the PCW problem in directed graphs that returns a rooted tree
whose prize-collecting cost is at most the optimum value of the
prize-collecting walks problem.
  We utilize our algorithm to develop combinatorial approximation algorithms
for two fundamental vehicle-routing problems (VRPs): (1) orienteering; and (2)
$k$-minimum-latency problem ($k$-MLP), wherein we seek to cover all nodes using
$k$ paths starting at a prescribed root node, so as to minimize the sum of the
node visiting times. Our combinatorial algorithm allows us to sidestep the part
where we solve a preflow-based LP in the LP-rounding algorithms of Friggstand
and Swamy (2017) for orienteering, and in the state-of-the-art
$7.183$-approximation algorithm for $k$-MP in Post and Swamy (2015).
Consequently, we obtain combinatorial implementations of these algorithms with
substantially improved running times compared with the current-best
approximation factors.
  We report computational results for our resulting (combinatorial
implementations of) orienteering algorithms, which show that the algorithms
perform quite well in practice, both in terms of the quality of the solution
they return, as also the upper bound they yield on the orienteering optimum
(which is obtained by leveraging the workings of our PCW algorithm).

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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: physics
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The categories of this paper are: math-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: math
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The categories of this paper are: bayes-an