185 research outputs found
Submodular Secretary Problems: {C}ardinality, Matching, and Linear Constraints
We study various generalizations of the secretary problem with submodular objective functions. Generally, a set of requests is revealed step-by-step to an algorithm in random order. For each request, one option has to be selected so as to maximize a monotone submodular function while ensuring feasibility. For our results, we assume that we are given an offline algorithm computing an -approximation for the respective problem. This way, we separate computational limitations from the ones due to the online nature. When only focusing on the online aspect, we can assume . In the submodular secretary problem, feasibility constraints are cardinality constraints. That is, out of a randomly ordered stream of entities, one has to select a subset size . For this problem, we present a -competitive algorithm for all , which asymptotically reaches competitive ratio for large . In submodular secretary matching, one side of a bipartite graph is revealed online. Upon arrival, each node has to be matched permanently to an offline node or discarded irrevocably. We give an -competitive algorithm. In both cases, we improve over previously best known competitive ratios, using a generalization of the algorithm for the classic secretary problem. Furthermore, we give an -competitive algorithm for submodular function maximization subject to linear packing constraints. Here, is the column sparsity, that is the maximal number of none-zero entries in a column of the constraint matrix, and is the minimal capacity of the constraints. Notably, this bound is independent of the total number of constraints. We improve the algorithm to be -competitive if both and are known to the algorithm beforehand
Packing Returning Secretaries
We study online secretary problems with returns in combinatorial packing
domains with candidates that arrive sequentially over time in random order.
The goal is to accept a feasible packing of candidates of maximum total value.
In the first variant, each candidate arrives exactly twice. All arrivals
occur in random order. We propose a simple 0.5-competitive algorithm that can
be combined with arbitrary approximation algorithms for the packing domain,
even when the total value of candidates is a subadditive function. For
bipartite matching, we obtain an algorithm with competitive ratio at least
for growing , and an algorithm with ratio at least
for all . We extend all algorithms and ratios to arrivals
per candidate.
In the second variant, there is a pool of undecided candidates. In each
round, a random candidate from the pool arrives. Upon arrival a candidate can
be either decided (accept/reject) or postponed (returned into the pool). We
mainly focus on minimizing the expected number of postponements when computing
an optimal solution. An expected number of is always
sufficient. For matroids, we show that the expected number can be reduced to
, where is the minimum of the ranks of matroid and
dual matroid. For bipartite matching, we show a bound of , where
is the size of the optimum matching. For general packing, we show a lower
bound of , even when the size of the optimum is .Comment: 23 pages, 5 figure
Wireless Network Stability in the SINR Model
We study the stability of wireless networks under stochastic arrival
processes of packets, and design efficient, distributed algorithms that achieve
stability in the SINR (Signal to Interference and Noise Ratio) interference
model.
Specifically, we make the following contributions. We give a distributed
algorithm that achieves -efficiency on all networks
(where is the number of links in the network), for all length monotone,
sub-linear power assignments. For the power control version of the problem, we
give a distributed algorithm with -efficiency (where is the length diversity of the link set).Comment: 10 pages, appeared in SIROCCO'1
Deterministic Digital Clustering of Wireless Ad Hoc Networks
We consider deterministic distributed communication in wireless ad hoc
networks of identical weak devices under the SINR model without predefined
infrastructure. Most algorithmic results in this model rely on various
additional features or capabilities, e.g., randomization, access to geographic
coordinates, power control, carrier sensing with various precision of
measurements, and/or interference cancellation. We study a pure scenario, when
no such properties are available. As a general tool, we develop a deterministic
distributed clustering algorithm. Our solution relies on a new type of
combinatorial structures (selectors), which might be of independent interest.
Using the clustering, we develop a deterministic distributed local broadcast
algorithm accomplishing this task in rounds, where
is the density of the network. To the best of our knowledge, this is
the first solution in pure scenario which is only polylog away from the
universal lower bound , valid also for scenarios with
randomization and other features. Therefore, none of these features
substantially helps in performing the local broadcast task. Using clustering,
we also build a deterministic global broadcast algorithm that terminates within
rounds, where is the diameter of the
network. This result is complemented by a lower bound , where is the path-loss parameter of the
environment. This lower bound shows that randomization or knowledge of own
location substantially help (by a factor polynomial in ) in the global
broadcast. Therefore, unlike in the case of local broadcast, some additional
model features may help in global broadcast
Distributed Deterministic Broadcasting in Uniform-Power Ad Hoc Wireless Networks
Development of many futuristic technologies, such as MANET, VANET, iThings,
nano-devices, depend on efficient distributed communication protocols in
multi-hop ad hoc networks. A vast majority of research in this area focus on
design heuristic protocols, and analyze their performance by simulations on
networks generated randomly or obtained in practical measurements of some
(usually small-size) wireless networks. %some library. Moreover, they often
assume access to truly random sources, which is often not reasonable in case of
wireless devices. In this work we use a formal framework to study the problem
of broadcasting and its time complexity in any two dimensional Euclidean
wireless network with uniform transmission powers. For the analysis, we
consider two popular models of ad hoc networks based on the
Signal-to-Interference-and-Noise Ratio (SINR): one with opportunistic links,
and the other with randomly disturbed SINR. In the former model, we show that
one of our algorithms accomplishes broadcasting in rounds, where
is the number of nodes and is the diameter of the network. If nodes
know a priori the granularity of the network, i.e., the inverse of the
maximum transmission range over the minimum distance between any two stations,
a modification of this algorithm accomplishes broadcasting in
rounds.
Finally, we modify both algorithms to make them efficient in the latter model
with randomly disturbed SINR, with only logarithmic growth of performance.
Ours are the first provably efficient and well-scalable, under the two
models, distributed deterministic solutions for the broadcast task.Comment: arXiv admin note: substantial text overlap with arXiv:1207.673
Online Independent Set Beyond the Worst-Case: Secretaries, Prophets, and Periods
We investigate online algorithms for maximum (weight) independent set on
graph classes with bounded inductive independence number like, e.g., interval
and disk graphs with applications to, e.g., task scheduling and spectrum
allocation. In the online setting, it is assumed that nodes of an unknown graph
arrive one by one over time. An online algorithm has to decide whether an
arriving node should be included into the independent set. Unfortunately, this
natural and practically relevant online problem cannot be studied in a
meaningful way within a classical competitive analysis as the competitive ratio
on worst-case input sequences is lower bounded by .
As a worst-case analysis is pointless, we study online independent set in a
stochastic analysis. Instead of focussing on a particular stochastic input
model, we present a generic sampling approach that enables us to devise online
algorithms achieving performance guarantees for a variety of input models. In
particular, our analysis covers stochastic input models like the secretary
model, in which an adversarial graph is presented in random order, and the
prophet-inequality model, in which a randomly generated graph is presented in
adversarial order. Our sampling approach bridges thus between stochastic input
models of quite different nature. In addition, we show that our approach can be
applied to a practically motivated admission control setting.
Our sampling approach yields an online algorithm for maximum independent set
with competitive ratio with respect to all of the mentioned
stochastic input models. for graph classes with inductive independence number
. The approach can be extended towards maximum-weight independent set by
losing only a factor of in the competitive ratio with denoting
the (expected) number of nodes
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Postmarket Surveillance of Medical Devices: A Comparison of Strategies in the US, EU, Japan, and China
Daniel Kramer and colleagues compare strategies for postmarket surveillance of medical devices and discuss ways to improve these systems. Please see later in the article for the Editors' Summar
Reading Articles Online
We study the online problem of reading articles that are listed in an
aggregated form in a dynamic stream, e.g., in news feeds, as abbreviated social
media posts, or in the daily update of new articles on arXiv. In such a
context, the brief information on an article in the listing only hints at its
content. We consider readers who want to maximize their information gain within
a limited time budget, hence either discarding an article right away based on
the hint or accessing it for reading. The reader can decide at any point
whether to continue with the current article or skip the remaining part
irrevocably. In this regard, Reading Articles Online, RAO, does differ
substantially from the Online Knapsack Problem, but also has its similarities.
Under mild assumptions, we show that any -competitive algorithm for the
Online Knapsack Problem in the random order model can be used as a black box to
obtain an -competitive algorithm for RAO, where
measures the accuracy of the hints with respect to the information profiles of
the articles. Specifically, with the current best algorithm for Online
Knapsack, which is -competitive, we obtain an upper bound
of on the competitive ratio of RAO. Furthermore, we study a
natural algorithm that decides whether or not to read an article based on a
single threshold value, which can serve as a model of human readers. We show
that this algorithmic technique is -competitive. Hence, our algorithms
are constant-competitive whenever the accuracy is a constant.Comment: Manuscript of COCOA 2020 pape
DISPATCH: An Optimally-Competitive Algorithm for Maximum Online Perfect Bipartite Matching with i.i.d. Arrivals
This work presents an optimally-competitive algorithm for the problem of
maximum weighted online perfect bipartite matching with i.i.d. arrivals. In
this problem, we are given a known set of workers, a distribution over job
types, and non-negative utility weights for each pair of worker and job types.
At each time step, a job is drawn i.i.d. from the distribution over job types.
Upon arrival, the job must be irrevocably assigned to a worker and cannot be
dropped. The goal is to maximize the expected sum of utilities after all jobs
are assigned.
We introduce DISPATCH, a 0.5-competitive, randomized algorithm. We also prove
that 0.5-competitive is the best possible. DISPATCH first selects a "preferred
worker" and assigns the job to this worker if it is available. The preferred
worker is determined based on an optimal solution to a fractional
transportation problem. If the preferred worker is not available, DISPATCH
randomly selects a worker from the available workers. We show that DISPATCH
maintains a uniform distribution over the workers even when the distribution
over the job types is non-uniform
The Imperative to Share Clinical Study Reports: Recommendations from the Tamiflu Experience
Peter Doshi and colleagues describe their experience trying and failing to access clinical study reports from the manufacturer of Tamiflu and challenge industry to defend their current position of RCT data secrecy
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