1,566 research outputs found
On Fast and Robust Information Spreading in the Vertex-Congest Model
This paper initiates the study of the impact of failures on the fundamental
problem of \emph{information spreading} in the Vertex-Congest model, in which
in every round, each of the nodes sends the same -bit message
to all of its neighbors.
Our contribution to coping with failures is twofold. First, we prove that the
randomized algorithm which chooses uniformly at random the next message to
forward is slow, requiring rounds on some graphs, which we
denote by , where is the vertex-connectivity.
Second, we design a randomized algorithm that makes dynamic message choices,
with probabilities that change over the execution. We prove that for
it requires only a near-optimal number of rounds, despite a
rate of failures per round. Our technique of choosing
probabilities that change according to the execution is of independent
interest.Comment: Appears in SIROCCO 2015 conferenc
Finding Connected Dense -Subgraphs
Given a connected graph on vertices and a positive integer ,
a subgraph of on vertices is called a -subgraph in . We design
combinatorial approximation algorithms for finding a connected -subgraph in
such that its density is at least a factor
of the density of the densest -subgraph
in (which is not necessarily connected). These particularly provide the
first non-trivial approximations for the densest connected -subgraph problem
on general graphs
Algorithmic and Hardness Results for the Colorful Components Problems
In this paper we investigate the colorful components framework, motivated by
applications emerging from comparative genomics. The general goal is to remove
a collection of edges from an undirected vertex-colored graph such that in
the resulting graph all the connected components are colorful (i.e., any
two vertices of the same color belong to different connected components). We
want to optimize an objective function, the selection of this function
being specific to each problem in the framework.
We analyze three objective functions, and thus, three different problems,
which are believed to be relevant for the biological applications: minimizing
the number of singleton vertices, maximizing the number of edges in the
transitive closure, and minimizing the number of connected components.
Our main result is a polynomial time algorithm for the first problem. This
result disproves the conjecture of Zheng et al. that the problem is -hard
(assuming ). Then, we show that the second problem is -hard,
thus proving and strengthening the conjecture of Zheng et al. that the problem
is -hard. Finally, we show that the third problem does not admit
polynomial time approximation within a factor of for
any , assuming (or within a factor of , assuming ).Comment: 18 pages, 3 figure
Quantum Interactive Proofs with Competing Provers
This paper studies quantum refereed games, which are quantum interactive
proof systems with two competing provers: one that tries to convince the
verifier to accept and the other that tries to convince the verifier to reject.
We prove that every language having an ordinary quantum interactive proof
system also has a quantum refereed game in which the verifier exchanges just
one round of messages with each prover. A key part of our proof is the fact
that there exists a single quantum measurement that reliably distinguishes
between mixed states chosen arbitrarily from disjoint convex sets having large
minimal trace distance from one another. We also show how to reduce the
probability of error for some classes of quantum refereed games.Comment: 13 pages, to appear in STACS 200
AMS measurements of cosmogenic and supernova-ejected radionuclides in deep-sea sediment cores
Samples of two deep-sea sediment cores from the Indian Ocean are analyzed
with accelerator mass spectrometry (AMS) to search for traces of recent
supernova activity around 2 Myr ago. Here, long-lived radionuclides, which are
synthesized in massive stars and ejected in supernova explosions, namely 26Al,
53Mn and 60Fe, are extracted from the sediment samples. The cosmogenic isotope
10Be, which is mainly produced in the Earths atmosphere, is analyzed for dating
purposes of the marine sediment cores. The first AMS measurement results for
10Be and 26Al are presented, which represent for the first time a detailed
study in the time period of 1.7-3.1 Myr with high time resolution. Our first
results do not support a significant extraterrestrial signal of 26Al above
terrestrial background. However, there is evidence that, like 10Be, 26Al might
be a valuable isotope for dating of deep-sea sediment cores for the past few
million years.Comment: 5 pages, 2 figures, Proceedings of the Heavy Ion Accelerator
Symposium on Fundamental and Applied Science, 2013, will be published by the
EPJ Web of conference
New Approximability Results for the Robust k-Median Problem
We consider a robust variant of the classical -median problem, introduced
by Anthony et al. \cite{AnthonyGGN10}. In the \emph{Robust -Median problem},
we are given an -vertex metric space and client sets . The objective is to open a set of
facilities such that the worst case connection cost over all client sets is
minimized; in other words, minimize . Anthony
et al.\ showed an approximation algorithm for any metric and
APX-hardness even in the case of uniform metric. In this paper, we show that
their algorithm is nearly tight by providing
approximation hardness, unless . This hardness result holds even for uniform and line
metrics. To our knowledge, this is one of the rare cases in which a problem on
a line metric is hard to approximate to within logarithmic factor. We
complement the hardness result by an experimental evaluation of different
heuristics that shows that very simple heuristics achieve good approximations
for realistic classes of instances.Comment: 19 page
Characterization of Binary Constraint System Games
We consider a class of nonlocal games that are related to binary constraint
systems (BCSs) in a manner similar to the games implicit in the work of Mermin
[N.D. Mermin, "Simple unified form for the major no-hidden-variables theorems,"
Phys. Rev. Lett., 65(27):3373-3376, 1990], but generalized to n binary
variables and m constraints. We show that, whenever there is a perfect
entangled protocol for such a game, there exists a set of binary observables
with commutations and products similar to those exhibited by Mermin. We also
show how to derive upper bounds strictly below 1 for the the maximum entangled
success probability of some BCS games. These results are partial progress
towards a larger project to determine the computational complexity of deciding
whether a given instance of a BCS game admits a perfect entangled strategy or
not.Comment: Revised version corrects an error in the previous version of the
proof of Theorem 1 that arises in the case of POVM measurement
Approximation Algorithms for Connected Maximum Cut and Related Problems
An instance of the Connected Maximum Cut problem consists of an undirected
graph G = (V, E) and the goal is to find a subset of vertices S V
that maximizes the number of edges in the cut \delta(S) such that the induced
graph G[S] is connected. We present the first non-trivial \Omega(1/log n)
approximation algorithm for the connected maximum cut problem in general graphs
using novel techniques. We then extend our algorithm to an edge weighted case
and obtain a poly-logarithmic approximation algorithm. Interestingly, in stark
contrast to the classical max-cut problem, we show that the connected maximum
cut problem remains NP-hard even on unweighted, planar graphs. On the positive
side, we obtain a polynomial time approximation scheme for the connected
maximum cut problem on planar graphs and more generally on graphs with bounded
genus.Comment: 17 pages, Conference version to appear in ESA 201
A Characterization of Visibility Graphs for Pseudo-Polygons
In this paper, we give a characterization of the visibility graphs of
pseudo-polygons. We first identify some key combinatorial properties of
pseudo-polygons, and we then give a set of five necessary conditions based off
our identified properties. We then prove that these necessary conditions are
also sufficient via a reduction to a characterization of vertex-edge visibility
graphs given by O'Rourke and Streinu
Implementation of higher-order absorbing boundary conditions for the Einstein equations
We present an implementation of absorbing boundary conditions for the
Einstein equations based on the recent work of Buchman and Sarbach. In this
paper, we assume that spacetime may be linearized about Minkowski space close
to the outer boundary, which is taken to be a coordinate sphere. We reformulate
the boundary conditions as conditions on the gauge-invariant
Regge-Wheeler-Zerilli scalars. Higher-order radial derivatives are eliminated
by rewriting the boundary conditions as a system of ODEs for a set of auxiliary
variables intrinsic to the boundary. From these we construct boundary data for
a set of well-posed constraint-preserving boundary conditions for the Einstein
equations in a first-order generalized harmonic formulation. This construction
has direct applications to outer boundary conditions in simulations of isolated
systems (e.g., binary black holes) as well as to the problem of
Cauchy-perturbative matching. As a test problem for our numerical
implementation, we consider linearized multipolar gravitational waves in TT
gauge, with angular momentum numbers l=2 (Teukolsky waves), 3 and 4. We
demonstrate that the perfectly absorbing boundary condition B_L of order L=l
yields no spurious reflections to linear order in perturbation theory. This is
in contrast to the lower-order absorbing boundary conditions B_L with L<l,
which include the widely used freezing-Psi_0 boundary condition that imposes
the vanishing of the Newman-Penrose scalar Psi_0.Comment: 25 pages, 9 figures. Minor clarifications. Final version to appear in
Class. Quantum Grav
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