Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minmax Regret for sink location on paths with general capacities   In dynamic flow networks, every vertex starts with items (flow) that need to
be shipped to designated sinks.
  All edges have two associated quantities: length, the amount of time required
for a particle to traverse the edge, and capacity, the number of units of flow
that can enter the edge in unit time. The goal is move all flow to the sinks. A
variation of the problem, modelling evacuation protocols, is to find the sink
location(s) that minimize evacuation time, restricting the flow to be
CONFLUENT. Solving this problem is is NP-hard on general graphs, and thus
research into optimal algorithms has traditionally been restricted to special
graphs such as paths, and trees.
  A specialized version of robust optimization is minmax REGRET, in which the
input flows at the vertices are only partially defined by constraints. The goal
is to find a sink location that has the minimum{ regret} over all input flows
that satisfy the partially defined constraints. Regret for a fully defined
input flow and a sink is defined to be the difference between the evacuation
time to that sink and the optimal evacuation time.
  A large recent literature derives polynomial time algorithms for the minmax
regret $k$-sink location problem on paths and trees under the simplifying
condition that all edges have the same (uniform) capacity.
  This paper develops a $O(n^4 \log n)$ time algorithm for the minmax regret
$1$-sink problem on paths with general (non-uniform) capacities. To the best of
our knowledge, this is the first minmax regret result for dynamic flow problems
in any type of graph with general capacities.

21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
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The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
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The categories of this paper are: eess
2
The categories of this paper are: math
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
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The categories of this paper are: q-fin