1,867 research outputs found
On the Number of Iterations for Dantzig-Wolfe Optimization and Packing-Covering Approximation Algorithms
We give a lower bound on the iteration complexity of a natural class of
Lagrangean-relaxation algorithms for approximately solving packing/covering
linear programs. We show that, given an input with random 0/1-constraints
on variables, with high probability, any such algorithm requires
iterations to compute a
-approximate solution, where is the width of the input.
The bound is tight for a range of the parameters .
The algorithms in the class include Dantzig-Wolfe decomposition, Benders'
decomposition, Lagrangean relaxation as developed by Held and Karp [1971] for
lower-bounding TSP, and many others (e.g. by Plotkin, Shmoys, and Tardos [1988]
and Grigoriadis and Khachiyan [1996]). To prove the bound, we use a discrepancy
argument to show an analogous lower bound on the support size of
-approximate mixed strategies for random two-player zero-sum
0/1-matrix games
Bottleneck Routing Games with Low Price of Anarchy
We study {\em bottleneck routing games} where the social cost is determined
by the worst congestion on any edge in the network. In the literature,
bottleneck games assume player utility costs determined by the worst congested
edge in their paths. However, the Nash equilibria of such games are inefficient
since the price of anarchy can be very high and proportional to the size of the
network. In order to obtain smaller price of anarchy we introduce {\em
exponential bottleneck games} where the utility costs of the players are
exponential functions of their congestions. We find that exponential bottleneck
games are very efficient and give a poly-log bound on the price of anarchy:
, where is the largest path length in the
players' strategy sets and is the set of edges in the graph. By adjusting
the exponential utility costs with a logarithm we obtain games whose player
costs are almost identical to those in regular bottleneck games, and at the
same time have the good price of anarchy of exponential games.Comment: 12 page
The detection of tethered and rising bubbles using multiple acoustic techniques
There exists a range of acoustic techniques for characterizing bubble populations within liquids. Each technique has limitations, and complete characterization of a population requires the sequential or simultaneous use of several, so that the limitations of each find compensation in the others. Here, nine techniques are deployed using one experimental rig, and compared to determine how accurately and rapidly they can characterize given bubble populations. These are, specifically (i) two stationary bubbles attached to a wire; and (ii) injected, rising bubble
Vertex Sparsifiers: New Results from Old Techniques
Given a capacitated graph and a set of terminals ,
how should we produce a graph only on the terminals so that every
(multicommodity) flow between the terminals in could be supported in
with low congestion, and vice versa? (Such a graph is called a
flow-sparsifier for .) What if we want to be a "simple" graph? What if
we allow to be a convex combination of simple graphs?
Improving on results of Moitra [FOCS 2009] and Leighton and Moitra [STOC
2010], we give efficient algorithms for constructing: (a) a flow-sparsifier
that maintains congestion up to a factor of , where , (b) a convex combination of trees over the terminals that maintains
congestion up to a factor of , and (c) for a planar graph , a
convex combination of planar graphs that maintains congestion up to a constant
factor. This requires us to give a new algorithm for the 0-extension problem,
the first one in which the preimages of each terminal are connected in .
Moreover, this result extends to minor-closed families of graphs.
Our improved bounds immediately imply improved approximation guarantees for
several terminal-based cut and ordering problems.Comment: An extended abstract appears in the 13th International Workshop on
Approximation Algorithms for Combinatorial Optimization Problems (APPROX),
2010. Final version to appear in SIAM J. Computin
Does the Babcock--Leighton Mechanism Operate on the Sun?
The contribution of the Babcock-Leighton mechanism to the generation of the
Sun's poloidal magnetic field is estimated from sunspot data for three solar
cycles. Comparison of the derived quantities with the A-index of the
large-scale magnetic field suggests a positive answer to the question posed in
the title of this paper.Comment: 5 pages, 2 figures, to apper in Astronomy Letter
Gravitational Helioseismology?
The magnitudes of the external gravitational perturbations associated with
the normal modes of the Sun are evaluated to determine whether these solar
oscillations could be observed with the proposed Laser Interferometer Space
Antenna (LISA), a network of satellites designed to detect gravitational
radiation. The modes of relevance to LISA---the , low-order , and
-modes---have not been conclusively observed to date. We find that the
energy in these modes must be greater than about in order
to be observable above the LISA detector noise. These mode energies are larger
than generally expected, but are much smaller than the current observational
upper limits. LISA may be confusion-limited at the relevant frequencies due to
the galactic background from short-period white dwarf binaries. Present
estimates of the number of these binaries would require the solar modes to have
energies above about to be observable by LISA.Comment: 8 pages; prepared with REVTEX 3.0 LaTeX macro
The Geometry of Entanglement Sudden Death
In open quantum systems, entanglement can vanish faster than coherence. This
phenomenon is usually called sudden death of entanglement. In this paper sudden
death of entanglement is discussed from a geometrical point of view, in the
context of two qubits. A classification of possible scenarios is presented,
with important known examples classified. Theoretical and experimental
construction of other examples is suggested as well as large dimensional and
multipartite versions of the effect.Comment: 6 pages, 2 figures, references added, initial paragraph corrected,
sectioning adopted, some parts rewritten; accepted by New J. Phy
- …