295 research outputs found
Risk-Averse Matchings over Uncertain Graph Databases
A large number of applications such as querying sensor networks, and
analyzing protein-protein interaction (PPI) networks, rely on mining uncertain
graph and hypergraph databases. In this work we study the following problem:
given an uncertain, weighted (hyper)graph, how can we efficiently find a
(hyper)matching with high expected reward, and low risk?
This problem naturally arises in the context of several important
applications, such as online dating, kidney exchanges, and team formation. We
introduce a novel formulation for finding matchings with maximum expected
reward and bounded risk under a general model of uncertain weighted
(hyper)graphs that we introduce in this work. Our model generalizes
probabilistic models used in prior work, and captures both continuous and
discrete probability distributions, thus allowing to handle privacy related
applications that inject appropriately distributed noise to (hyper)edge
weights. Given that our optimization problem is NP-hard, we turn our attention
to designing efficient approximation algorithms. For the case of uncertain
weighted graphs, we provide a -approximation algorithm, and a
-approximation algorithm with near optimal run time. For the case
of uncertain weighted hypergraphs, we provide a
-approximation algorithm, where is the rank of the
hypergraph (i.e., any hyperedge includes at most nodes), that runs in
almost (modulo log factors) linear time.
We complement our theoretical results by testing our approximation algorithms
on a wide variety of synthetic experiments, where we observe in a controlled
setting interesting findings on the trade-off between reward, and risk. We also
provide an application of our formulation for providing recommendations of
teams that are likely to collaborate, and have high impact.Comment: 25 page
Finding Densest -Connected Subgraphs
Dense subgraph discovery is an important graph-mining primitive with a
variety of real-world applications. One of the most well-studied optimization
problems for dense subgraph discovery is the densest subgraph problem, where
given an edge-weighted undirected graph , we are asked to find
that maximizes the density , i.e., half the weighted
average degree of the induced subgraph . This problem can be solved
exactly in polynomial time and well-approximately in almost linear time.
However, a densest subgraph has a structural drawback, namely, the subgraph may
not be robust to vertex/edge failure. Indeed, a densest subgraph may not be
well-connected, which implies that the subgraph may be disconnected by removing
only a few vertices/edges within it. In this paper, we provide an algorithmic
framework to find a dense subgraph that is well-connected in terms of
vertex/edge connectivity. Specifically, we introduce the following problems:
given a graph and a positive integer/real , we are asked to find
that maximizes the density under the constraint that
is -vertex/edge-connected. For both problems, we propose
polynomial-time (bicriteria and ordinary) approximation algorithms, using
classic Mader's theorem in graph theory and its extensions
Evaluation of the quantiles and superquantiles of the makespan in interval valued activity networks
This paper deals with the evaluation of quantile-based risk measures for the
makespan in scheduling problems represented as temporal networks with uncer tainties on the activity durations. More specifically, for each activity only the
interval for its possible duration values is known in advance to both the sched uler and the risk analyst. Given a feasible schedule, we calculate the quantiles
and the superquantiles of the makespan which are of interest as risk indicators
in various applications.
To this aim we propose and test a set of novel algorithms to determine rapid
and accurate numerical estimations based on the calculation of theoretically
proven lower and upper bounds. An extensive experimental campaign compu tationally shows the validity of the proposed methods, and allows to highlight
their performances through the comparison with respect to the state-of-the-art
algorithms
05201 Abstracts Collection -- Design and Analysis of Randomized and Approximation Algorithms
From 15.05.05 to 20.05.05, the Dagstuhl Seminar 05201 ``Design and Analysis of Randomized and Approximation Algorithms\u27\u27 was held
in the International Conference and Research Center (IBFI),
Schloss Dagstuhl.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available
Finding a Collective Set of Items: From Proportional Multirepresentation to Group Recommendation
We consider the following problem: There is a set of items (e.g., movies) and
a group of agents (e.g., passengers on a plane); each agent has some intrinsic
utility for each of the items. Our goal is to pick a set of items that
maximize the total derived utility of all the agents (i.e., in our example we
are to pick movies that we put on the plane's entertainment system).
However, the actual utility that an agent derives from a given item is only a
fraction of its intrinsic one, and this fraction depends on how the agent ranks
the item among the chosen, available, ones. We provide a formal specification
of the model and provide concrete examples and settings where it is applicable.
We show that the problem is hard in general, but we show a number of
tractability results for its natural special cases
Graph Algorithms and Applications
The mixture of data in real-life exhibits structure or connection property in nature. Typical data include biological data, communication network data, image data, etc. Graphs provide a natural way to represent and analyze these types of data and their relationships. Unfortunately, the related algorithms usually suffer from high computational complexity, since some of these problems are NP-hard. Therefore, in recent years, many graph models and optimization algorithms have been proposed to achieve a better balance between efficacy and efficiency. This book contains some papers reporting recent achievements regarding graph models, algorithms, and applications to problems in the real world, with some focus on optimization and computational complexity
Stochastic Solutions for Dense Subgraph Discovery in Multilayer Networks
Network analysis has played a key role in knowledge discovery and data
mining. In many real-world applications in recent years, we are interested in
mining multilayer networks, where we have a number of edge sets called layers,
which encode different types of connections and/or time-dependent connections
over the same set of vertices. Among many network analysis techniques, dense
subgraph discovery, aiming to find a dense component in a network, is an
essential primitive with a variety of applications in diverse domains. In this
paper, we introduce a novel optimization model for dense subgraph discovery in
multilayer networks. Our model aims to find a stochastic solution, i.e., a
probability distribution over the family of vertex subsets, rather than a
single vertex subset, whereas it can also be used for obtaining a single vertex
subset. For our model, we design an LP-based polynomial-time exact algorithm.
Moreover, to handle large-scale networks, we also devise a simple, scalable
preprocessing algorithm, which often reduces the size of the input networks
significantly and results in a substantial speed-up. Computational experiments
demonstrate the validity of our model and the effectiveness of our algorithms.Comment: Accepted to WSDM 202
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