8,039 research outputs found
Efficiently Clustering Very Large Attributed Graphs
Attributed graphs model real networks by enriching their nodes with
attributes accounting for properties. Several techniques have been proposed for
partitioning these graphs into clusters that are homogeneous with respect to
both semantic attributes and to the structure of the graph. However, time and
space complexities of state of the art algorithms limit their scalability to
medium-sized graphs. We propose SToC (for Semantic-Topological Clustering), a
fast and scalable algorithm for partitioning large attributed graphs. The
approach is robust, being compatible both with categorical and with
quantitative attributes, and it is tailorable, allowing the user to weight the
semantic and topological components. Further, the approach does not require the
user to guess in advance the number of clusters. SToC relies on well known
approximation techniques such as bottom-k sketches, traditional graph-theoretic
concepts, and a new perspective on the composition of heterogeneous distance
measures. Experimental results demonstrate its ability to efficiently compute
high-quality partitions of large scale attributed graphs.Comment: This work has been published in ASONAM 2017. This version includes an
appendix with validation of our attribute model and distance function,
omitted in the converence version for lack of space. Please refer to the
published versio
Estimating operator norms using covering nets
We present several polynomial- and quasipolynomial-time approximation schemes
for a large class of generalized operator norms. Special cases include the
norm of matrices for , the support function of the set of
separable quantum states, finding the least noisy output of
entanglement-breaking quantum channels, and approximating the injective tensor
norm for a map between two Banach spaces whose factorization norm through
is bounded.
These reproduce and in some cases improve upon the performance of previous
algorithms by Brand\~ao-Christandl-Yard and followup work, which were based on
the Sum-of-Squares hierarchy and whose analysis used techniques from quantum
information such as the monogamy principle of entanglement. Our algorithms, by
contrast, are based on brute force enumeration over carefully chosen covering
nets. These have the advantage of using less memory, having much simpler proofs
and giving new geometric insights into the problem. Net-based algorithms for
similar problems were also presented by Shi-Wu and Barak-Kelner-Steurer, but in
each case with a run-time that is exponential in the rank of some matrix. We
achieve polynomial or quasipolynomial runtimes by using the much smaller nets
that exist in spaces. This principle has been used in learning theory,
where it is known as Maurey's empirical method.Comment: 24 page
Pricing caps with HJM models: the benefits of humped volatility
In this paper we compare different multifactor HJM models with humped volatility structures, to each other and to models with strictly decreasing volatility. All the models are estimated on Euribor and swap rates panel data. We develop the analysis in two steps: first we study the in-sample properties of the estimated models, then we study the pricing performance on caps. We find the humped volatility specification to greatly improve the model estimation and to provide sufficiently accurate cap prices, although the models has been calibrated on interest rates data and not on cap prices. Moreover we find the two factor humped volatility model to outperform the three factor models in pricing capsFinance, interest rates, humped volatility, Kalman filter, cap and floor pricing
The Non-Uniform k-Center Problem
In this paper, we introduce and study the Non-Uniform k-Center problem
(NUkC). Given a finite metric space and a collection of balls of radii
, the NUkC problem is to find a placement of their
centers on the metric space and find the minimum dilation , such that
the union of balls of radius around the th center covers
all the points in . This problem naturally arises as a min-max vehicle
routing problem with fleets of different speeds.
The NUkC problem generalizes the classic -center problem when all the
radii are the same (which can be assumed to be after scaling). It also
generalizes the -center with outliers (kCwO) problem when there are
balls of radius and balls of radius . There are -approximation
and -approximation algorithms known for these problems respectively; the
former is best possible unless P=NP and the latter remains unimproved for 15
years.
We first observe that no -approximation is to the optimal dilation is
possible unless P=NP, implying that the NUkC problem is more non-trivial than
the above two problems. Our main algorithmic result is an
-bi-criteria approximation result: we give an -approximation
to the optimal dilation, however, we may open centers of each
radii. Our techniques also allow us to prove a simple (uni-criteria), optimal
-approximation to the kCwO problem improving upon the long-standing
-factor. Our main technical contribution is a connection between the NUkC
problem and the so-called firefighter problems on trees which have been studied
recently in the TCS community.Comment: Adjusted the figur
Stable Secretaries
We define and study a new variant of the secretary problem. Whereas in the
classic setting multiple secretaries compete for a single position, we study
the case where the secretaries arrive one at a time and are assigned, in an
on-line fashion, to one of multiple positions. Secretaries are ranked according
to talent, as in the original formulation, and in addition positions are ranked
according to attractiveness. To evaluate an online matching mechanism, we use
the notion of blocking pairs from stable matching theory: our goal is to
maximize the number of positions (or secretaries) that do not take part in a
blocking pair. This is compared with a stable matching in which no blocking
pair exists. We consider the case where secretaries arrive randomly, as well as
that of an adversarial arrival order, and provide corresponding upper and lower
bounds.Comment: Accepted for presentation at the 18th ACM conference on Economics and
Computation (EC 2017
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