69,335 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
Best of Two Local Models: Local Centralized and Local Distributed Algorithms
We consider two models of computation: centralized local algorithms and local
distributed algorithms. Algorithms in one model are adapted to the other model
to obtain improved algorithms.
Distributed vertex coloring is employed to design improved centralized local
algorithms for: maximal independent set, maximal matching, and an approximation
scheme for maximum (weighted) matching over bounded degree graphs. The
improvement is threefold: the algorithms are deterministic, stateless, and the
number of probes grows polynomially in , where is the number of
vertices of the input graph.
The recursive centralized local improvement technique by Nguyen and
Onak~\cite{onak2008} is employed to obtain an improved distributed
approximation scheme for maximum (weighted) matching. The improvement is
twofold: we reduce the number of rounds from to for a
wide range of instances and, our algorithms are deterministic rather than
randomized
Linear Programming in the Semi-streaming Model with Application to the Maximum Matching Problem
In this paper, we study linear programming based approaches to the maximum
matching problem in the semi-streaming model. The semi-streaming model has
gained attention as a model for processing massive graphs as the importance of
such graphs has increased. This is a model where edges are streamed-in in an
adversarial order and we are allowed a space proportional to the number of
vertices in a graph.
In recent years, there has been several new results in this semi-streaming
model. However broad techniques such as linear programming have not been
adapted to this model. We present several techniques to adapt and optimize
linear programming based approaches in the semi-streaming model with an
application to the maximum matching problem. As a consequence, we improve
(almost) all previous results on this problem, and also prove new results on
interesting variants
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