11,434 research outputs found
Space- and Time-Efficient Algorithm for Maintaining Dense Subgraphs on One-Pass Dynamic Streams
While in many graph mining applications it is crucial to handle a stream of
updates efficiently in terms of {\em both} time and space, not much was known
about achieving such type of algorithm. In this paper we study this issue for a
problem which lies at the core of many graph mining applications called {\em
densest subgraph problem}. We develop an algorithm that achieves time- and
space-efficiency for this problem simultaneously. It is one of the first of its
kind for graph problems to the best of our knowledge.
In a graph , the "density" of a subgraph induced by a subset of
nodes is defined as , where is the set of
edges in with both endpoints in . In the densest subgraph problem, the
goal is to find a subset of nodes that maximizes the density of the
corresponding induced subgraph. For any , we present a dynamic
algorithm that, with high probability, maintains a -approximation
to the densest subgraph problem under a sequence of edge insertions and
deletions in a graph with nodes. It uses space, and has an
amortized update time of and a query time of . Here,
hides a O(\poly\log_{1+\epsilon} n) term. The approximation ratio
can be improved to at the cost of increasing the query time to
. It can be extended to a -approximation
sublinear-time algorithm and a distributed-streaming algorithm. Our algorithm
is the first streaming algorithm that can maintain the densest subgraph in {\em
one pass}. The previously best algorithm in this setting required
passes [Bahmani, Kumar and Vassilvitskii, VLDB'12]. The space required by our
algorithm is tight up to a polylogarithmic factor.Comment: A preliminary version of this paper appeared in STOC 201
Community detection in complex networks using Extremal Optimization
We propose a novel method to find the community structure in complex networks
based on an extremal optimization of the value of modularity. The method
outperforms the optimal modularity found by the existing algorithms in the
literature. We present the results of the algorithm for computer simulated and
real networks and compare them with other approaches. The efficiency and
accuracy of the method make it feasible to be used for the accurate
identification of community structure in large complex networks.Comment: 4 pages, 4 figure
Structure of 10N in 9C+p resonance scattering
The structure of exotic nucleus 10N was studied using 9C+p resonance
scattering. Two L=0 resonances were found to be the lowest states in 10N. The
ground state of 10N is unbound with respect to proton decay by 2.2(2) or 1.9(2)
MeV depending on the 2- or 1- spin-parity assignment, and the first excited
state is unbound by 2.8(2) MeV.Comment: 6 pages, 4 figures, 1 table, submitted to Phys. Lett.
Nuclear structure beyond the neutron drip line: the lowest energy states in He via their T=5/2 isobaric analogs in Li
The level structure of the very neutron rich and unbound He nucleus has
been the subject of significant experimental and theoretical study. Many recent
works have claimed that the two lowest energy He states exist with spins
and and widths on the order of hundreds of keV.
These findings cannot be reconciled with our contemporary understanding of
nuclear structure. The present work is the first high-resolution study with low
statistical uncertainty of the relevant excitation energy range in the
He system, performed via a search for the T=5/2 isobaric analog states
in Li populated through He+p elastic scattering. The present data show
no indication of any narrow structures. Instead, we find evidence for a broad
state in He located approximately 3 MeV above the neutron
decay threshold
Shortest Path Computation with No Information Leakage
Shortest path computation is one of the most common queries in location-based
services (LBSs). Although particularly useful, such queries raise serious
privacy concerns. Exposing to a (potentially untrusted) LBS the client's
position and her destination may reveal personal information, such as social
habits, health condition, shopping preferences, lifestyle choices, etc. The
only existing method for privacy-preserving shortest path computation follows
the obfuscation paradigm; it prevents the LBS from inferring the source and
destination of the query with a probability higher than a threshold. This
implies, however, that the LBS still deduces some information (albeit not
exact) about the client's location and her destination. In this paper we aim at
strong privacy, where the adversary learns nothing about the shortest path
query. We achieve this via established private information retrieval
techniques, which we treat as black-box building blocks. Experiments on real,
large-scale road networks assess the practicality of our schemes.Comment: VLDB201
Statistics of Oscillator Strengths in Chaotic Systems
The statistical description of oscillator strengths for systems like hydrogen
in a magnetic field is developed by using the supermatrix nonlinear
-model. The correlator of oscillator strengths is found to have a
universal parametric and frequency dependence, and its analytical expression is
given. This universal expression applies to quantum chaotic systems with the
same generality as Wigner-Dyson statistics.Comment: 11 pages, REVTeX3+epsf, two EPS figures. Replaced by the published
version. Minor changes
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Minimum Cost Flows in Graphs with Unit Capacities
We consider the minimum cost flow problem on graphs with unit capacities and its special cases. In previous studies, special purpose algorithms exploiting the fact that capacities are one have been developed.
In contrast, for maximum flow with unit capacities, the best bounds are proven for slight modifications of classical blocking flow and push-relabel algorithms.
In this paper we show that the classical cost scaling algorithms of Goldberg and Tarjan (for general integer capacities) applied to a problem with unit capacities achieve or improve the best known bounds.
For weighted bipartite matching we establish a bound of O(sqrt{rm}log C) on a slight variation of this algorithm. Here r is the size of the smaller side of the bipartite graph, m is the number of edges, and C is the largest absolute value of an arc-cost. This simplifies a result of [Duan et al. 2011] and improves the bound, answering an open question of [Tarjan and Ramshaw 2012]. For graphs with unit vertex capacities we establish a novel O(sqrt{n}mlog(nC)) bound. We also give the first cycle canceling algorithm for minimum cost flow with unit capacities. The algorithm naturally generalizes the single source shortest path algorithm of [Goldberg 1995]
Absorption of mass and angular momentum by a black hole: Time-domain formalisms for gravitational perturbations, and the small-hole/slow-motion approximation
The first objective of this work is to obtain practical prescriptions to
calculate the absorption of mass and angular momentum by a black hole when
external processes produce gravitational radiation. These prescriptions are
formulated in the time domain within the framework of black-hole perturbation
theory. Two such prescriptions are presented. The first is based on the
Teukolsky equation and it applies to general (rotating) black holes. The second
is based on the Regge-Wheeler and Zerilli equations and it applies to
nonrotating black holes. The second objective of this work is to apply the
time-domain absorption formalisms to situations in which the black hole is
either small or slowly moving. In the context of this small-hole/slow-motion
approximation, the equations of black-hole perturbation theory can be solved
analytically, and explicit expressions can be obtained for the absorption of
mass and angular momentum. The changes in the black-hole parameters can then be
understood in terms of an interaction between the tidal gravitational fields
supplied by the external universe and the hole's tidally-induced mass and
current quadrupole moments. For a nonrotating black hole the quadrupole moments
are proportional to the rate of change of the tidal fields on the hole's world
line. For a rotating black hole they are proportional to the tidal fields
themselves.Comment: 36 pages, revtex4, no figures, final published versio
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