6,761 research outputs found
Stochastic Vehicle Routing with Recourse
We study the classic Vehicle Routing Problem in the setting of stochastic
optimization with recourse. StochVRP is a two-stage optimization problem, where
demand is satisfied using two routes: fixed and recourse. The fixed route is
computed using only a demand distribution. Then after observing the demand
instantiations, a recourse route is computed -- but costs here become more
expensive by a factor lambda.
We present an O(log^2 n log(n lambda))-approximation algorithm for this
stochastic routing problem, under arbitrary distributions. The main idea in
this result is relating StochVRP to a special case of submodular orienteering,
called knapsack rank-function orienteering. We also give a better approximation
ratio for knapsack rank-function orienteering than what follows from prior
work. Finally, we provide a Unique Games Conjecture based omega(1) hardness of
approximation for StochVRP, even on star-like metrics on which our algorithm
achieves a logarithmic approximation.Comment: 20 Pages, 1 figure Revision corrects the statement and proof of
Theorem 1.
Observer Placement for Source Localization: The Effect of Budgets and Transmission Variance
When an epidemic spreads in a network, a key question is where was its
source, i.e., the node that started the epidemic. If we know the time at which
various nodes were infected, we can attempt to use this information in order to
identify the source. However, maintaining observer nodes that can provide their
infection time may be costly, and we may have a budget on the number of
observer nodes we can maintain. Moreover, some nodes are more informative than
others due to their location in the network. Hence, a pertinent question
arises: Which nodes should we select as observers in order to maximize the
probability that we can accurately identify the source? Inspired by the simple
setting in which the node-to-node delays in the transmission of the epidemic
are deterministic, we develop a principled approach for addressing the problem
even when transmission delays are random. We show that the optimal
observer-placement differs depending on the variance of the transmission delays
and propose approaches in both low- and high-variance settings. We validate our
methods by comparing them against state-of-the-art observer-placements and show
that, in both settings, our approach identifies the source with higher
accuracy.Comment: Accepted for presentation at the 54th Annual Allerton Conference on
Communication, Control, and Computin
Sticky Seeding in Discrete-Time Reversible-Threshold Networks
When nodes can repeatedly update their behavior (as in agent-based models
from computational social science or repeated-game play settings) the problem
of optimal network seeding becomes very complex. For a popular
spreading-phenomena model of binary-behavior updating based on thresholds of
adoption among neighbors, we consider several planning problems in the design
of \textit{Sticky Interventions}: when adoption decisions are reversible, the
planner aims to find a Seed Set where temporary intervention leads to long-term
behavior change. We prove that completely converting a network at minimum cost
is -hard to approximate and that maximizing conversion
subject to a budget is -hard to approximate. Optimization
heuristics which rely on many objective function evaluations may still be
practical, particularly in relatively-sparse networks: we prove that the
long-term impact of a Seed Set can be evaluated in operations. For a
more descriptive model variant in which some neighbors may be more influential
than others, we show that under integer edge weights from
objective function evaluation requires only operations. These
operation bounds are based on improvements we give for bounds on
time-steps-to-convergence under discrete-time reversible-threshold updates in
networks.Comment: 19 pages, 2 figure
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